Mega Probability PowerPoint

Mega Probability PowerPoint
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Menu Probability as fractions Listing outcomes
Experimental Probability Mutually Exclusive Events Sample Space diagrams Tree diagrams Independent events Tree diagrams 2 Dependent events Quizzes

Quizzes Probability of events NOT happening Expected outcomes
Mutually exclusive events Probability of a die The probability scale Relative Frequency Tree diagrams Home

Experimental Probability
We use experimental probability to estimate probability and make predictions. First we do an experiment, then we work out the probability, we can then use this to work out what we expect to see in the future.

4 x 0.2 8 0.08 A) B) 0.8 80 C) D)

3 x 0.6 18 1.8 A) B) 0.18 0.018 C) D)

7 x 0.3 21 20.1 A) B) 0.21 2.1 C) D)

5 x 0.6 3 30 A) B) 0.30 0.3 C) D)

4 x 0.12 4.8 48 A) B) 40.8 0.48 C) D)

3 x 0.03 9 0.09 A) B) 9.00 0.9 C) D)

7 x 1.1 77 7.7 A) B) 0.77 7.07 C) D)

1.2 x 5 60 0.6 A) B) 0.60 6 C) D)

0.4 x 0.2 8 0.8 A) B) 0.08 0.008 C) D)

0.8 x 0.7 0.56 56 A) B) 5.06 5.6 C) D)

Example I want to find the probability that the next car to go past will be blue: I need to spend time recording cars going past, and make a table: Next I divide then number of BLUE CARS by the TOTAL NUMBER OF CARS 4 ÷20= 0.2, this is the experimental probability Blue Red Green Black 4 5 2 9

Blue Cars The probability of a blue car is 0.2,
If 10 cars go past I expect to see 10 x 0.2= 2 blue cars If 40 cars go past I expect to see 40 x 0.2= 8 blue cars If 55 cars go past I expect to see 55 x 0.2= 11 blue cars

Think about.. Is this a good experiment? How could it be improved?
I want to fin out he probability of selecting someone who supports a team, so I ask ten of my friends: Man Utd West Brom Chelsea Scunthorpe 4 2 1 Is this a good experiment? How could it be improved? Does this mean there are more West Brom fans in the world than Chelsea fans? If I asked 1,000, 000 people how many Wolverhampton fans would I expect to find? This is tricky, they might not own up to it, I know I wouldn’t want to

Mutually Exclusive Probabilities

Mutualy Exclusive Events
We say that events are mutually exclusive if they cannot happen at the same time. You cannot You cannot win and loose the same football match You cannot catch the bus and miss it

Mutually exclusive probabilities will always add to:
1 whole or 100%

P(event not happening) 0.6 0.4 20% 80%
Events not happening The probability of an event happening and the probability of it NOT happening will always add to 1 whole (or 100%) because the two events are mutually exclusive. P(event) P(event not happening) 0.6 0.4 20% 80% 3 5 2 5

Example 1 Andy and Jill are playing a game. There has to be a winner (there are no draws). The probability that Andy will win is 45% what is the probability Jill will win? The probabilities must add to make 100% 45% + X = 100% The probability that Jill will win is 55% X = 55%

Example 2 Andy and Jill are playing another game. This time they can draw. The probability that Andy will win is 32% the probability Jill will win is 25%. What is the probability of a draw? The probabilities must add to make 100% 32% + 25% + X= 100% The probability that Jill will win is 43% 57% + X= 100% X = 43%

Example 3 The probabilities must add to make 1 0.2 + 0.4 + X=1
There are some balls in a bag (red, yellow and green). The probability that a yellow ball is picked out is 0.2, the probability a green ball is picked out is 0.4, what is the probability a red ball will come out? The probabilities must add to make 1 X=1 The probability that a red ball will come out is 0.4 X = 0.4

Questions ANSWERS 0.7 0.6 0.48 0.79 75% 2% 3/5 4/10 3/15
Mutually exclusive Not mutually exclusive 0.1 0.2 0.23 0.24

Sample space diagrams

Sample space diagrams We use sample space diagrams to make our life easier when we are dealing with the probability of two things happening. For example tossing two coins or rolling two dice or spinning two spinners A sample space diagram makes sure we don’t forget any outcomes and makes it easy for us to work out probabilities

Tossing a coin and rolling a dice
Heads Tails 1 H1 T1 2 H2 T2 3 H3 T3 4 H4 T4 5 H5 T5 6 H6 T6 There are 12 spaces in our diagram, so every probability will start out over 12. 1 12 What’s the probability of getting a heads and a 3? 3 12 1 4 What’s the probability of getting a tails and an even number? =

You roll two dice, and add their scores, what could you get?
+ 1 2 3 4 5 6 + 1 2 3 4 5 6 7 8 9 10 11 12 Dice 2 We can use this diagram to see which numbers are most likely to come up What number appears the most? What numbers appears the least?

Reading off probabilities
Dice 1 + 1 2 3 4 5 6 7 8 9 10 11 12 Dice 2 There are 36 spaces in our diagram, so every probability will start out over 36. 6 36 = 1 6 What’s the probability of scoring 7? 4 36 = 1 9 What’s the probability of scoring 5? 6 36 = 1 6 What’s the probability of less 5?

Questions ANSWERS 1/36 1/12 1/9 7, it appears the most 6/25 19/25 9/25
6/25 19/25 9/25 8/25

Writing Probabilities
Probability Writing Probabilities

Likely Unlikely Impossible Possible Probably Definite Certain Probable
Using words Write down how many words relating to probability as you can in 1 min Likely Unlikely Impossible Possible Probably Definite Certain Probable

Using Numbers Our aim is to find a more accurate way to describe probabilities If I picked something out of the bag, what is the chance it will be a sweet? 50% 1 2

What is the probability that I will pick out a sweet?
Using Fractions What is the probability that I will pick out a sweet?

REMEMBER TO CANCEL DOWN!

Where should these Probabilities go?
Impossible Unlikely 50 / 50 Likely Certain 1 2 5 1 8 4 8 9 18 20 4 12 13 26 75 100 126 500

Probability as Fractions
ANSWERS 3/10 1/5 4/5 7/10 1/20 1/13 4/13 5/13 1/26 5/52 3. I have a pack of card (without jokers) what is the probability I pick: A Red card A heart A Club A heart or a club A 2 A King A picture card A number card smaller than 6 A number card greater than 6 An even number An odd number A red number 3 A black Queen or red Jack A King of Hearts or a 5 I have some counters in a bag. There are 3 blue, 5 red and 2 green. What is the probability I pick out: A blue A red A green A purple A blue or red A red or green I am picking my socks at random today, I have 4 pairs with stripes on, 10 with spots, 5 with clowns and 1 with maths pictures. What is the probability I will pick out: Spotty socks Clown socks Maths Socks Clown or spotty socks Maths or stripe socks

Probability Listing Outcomes

A job to do... Principal Skinner has an important 2 person job that needs doing. Here are the kids he can choose from, write down all the different teams he could pick Bart Lisa Martin Milhouse

He could pick Bart and Lisa Lisa and Martin Lisa and Milhouse Martin and Nelson Was your list organised in a sensible way? It is very easy to forget just one line if you are not organised.

Homer’s dinner Homer’s out for dinner, he needs to pick a starter, main and pudding. Here is the menu: Starter: Shrimp Soup Salad Main: Lasagne Burger Pudding: Ice cream Fudge Cake List all of the things he could have

He could pick... Shrimp, Lasagne and Ice Cream Shrimp, Lasagne and Fudge Cake Shrimp, Burger and Ice Cream Shrimp, Burger and Fudge Cake Soup, Lasagne and Ice Cream Soup, Lasagne and Fudge Cake Soup, Burger and Ice Cream Soup, Burger and Fudge Cake Salad, Lasagne and Ice Cream Salad, Lasagne and Fudge Cake Salad, Burger and Ice Cream Salad, Burger and Fudge Cake

Listing Outcomes ANSWERS H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6 1+1=2 1+2=3 1+3=4 2+1=3 2+2=4 2+3=5 3+1=4 3+2=5 3+3=6 Tb,Tt,Tc,Cb,Ct,Cc,Jb,Jt,Jc 4 8 64 2x 6 24 If I flip a coin and roll a dice, list all the possible outcomes I could get. I spin two fair spinners number 1 to 3. Copy and complete the table to show all the possible outcomes. When I have breakfast I have a drink and something to eat. The drinks I choose from are tea, coffee and juice and I eat a bagel, toast or cereal. Write down all the different combinations I could have for breakfast. If I toss 1 coin there are 2 possible outcomes, find the number of outcomes for: 2 coins b. 3 coins c. 4 coins d. X coins Lucy, Amy and George are going to have their photo taken so they sit in a line: How many different ways could they order themselves? Andy joins them, how many different ways could they order themselves now? Spinner 1 Spinner 2 Total

Tree diagrams

I have a bag with red and green counters
I have a bag with red and green counters. The probability I pick a red is 0.1, the probability I pick a green is 0.9. I pick a counter out, look a it, PUT IT BACK, and pick again. Draw a tree diagram for this situation. Pick 1 Pick 2 R P(RR)=0.1 x 0.1 = 0.01 0.1 R G P(RG)=0.1 x 0.9 = 0.09 0.9 0.1 0.09 P(GR)=0.9 x 0.1 = R 0.9 0.1 G P(G)=0.9 x 0.9 = 0.81 G 0.9

Pick 1 Pick 2 What is the probability that I pick one of each? 0.18 R
If this happens I get red then green OR green then red. When I see OR I know I have to add the probabilities So... P(RG) + P(GR) = = 0.18 Pick 1 Pick 2 R P(RR)=0.1 x 0.1 = 0.01 0.1 R G P(RG)=0.1 x 0.9 = 0.09 0.9 0.1 0.09 P(GR)=0.9 x 0.1 = R 0.9 0.1 G P(G)=0.9 x 0.9 = 0.81 G 0.9

I play two games of chess. The probability I win 0
I play two games of chess. The probability I win 0.8, the probability I loose is 0.2. My performance in the first game does not affect my performance in the second Draw a tree diagram for this situation. Game 1 Game 2 W P(WW)=0.8X0.8 0.64 0.8 W L P(WL)=0.8 x 0.2 = 0.16 0.2 0.8 0.16 P(LW)=0.2 x 0.8 = W 0.2 0.8 L P(LL)=0.2 x 0.2 = 0.04 L 0.2

Game 1 Game 2 What is the probability that I only win one game? 0.32 W
If this happens I will win then loose OR loose then win. When I see OR I know I have to add the probabilities So... P(WL) + P(LW) = = 0.32 Game 1 Game 2 W P(WW)=0.8X0.8 0.64 0.8 W L P(WL)=0.8 x 0.2 = 0.16 0.2 0.8 0.16 P(LW)=0.2 x 0.8 = W 0.2 0.8 L P(LL)=0.2 x 0.2 = 0.04 L 0.2

I play two games of pool. The probability I win is ¾
I play two games of pool. The probability I win is ¾. My performance in the first game does not affect my performance in the second Draw a tree diagram for this situation. Game 1 Game 2 W P(WW)=3/4 x 3/4 9/16 3/4 W L P(WL)=3/4 x 1/4 = 3/16 1/4 3/4 P(LW)=1/4 x 3/4= 3/16 W 1/4 3/4 L P(LL)=1/4 x 1/4= 1/16 L 1/4

Game 1 Game 2 What is the probability that I only win one game?
If this happens I will win then loose OR loose then win. When I see OR I know I have to add the probabilities So... P(WL) + P(LW) = 3/16 + 3/16= 6/16 or 3/8 Game 1 Game 2 W P(WW)=3/4 x 3/4 9/16 3/4 W L P(WL)=3/4 x 1/4 = 3/16 1/4 3/4 P(LW)=1/4 x 3/4= 3/16 W 1/4 3/4 L P(LL)=1/4 x 1/4= 1/16 L 1/4

Tree Diagrams ANSWERS 2. 169/400 49/400 91/400 0.4 0.8 3. a)0.12
b)0.08 c)0.32 1/12 1/6 7/44 4/121 14/121 93/242 A) I have a bag with 20 balls in, there are 13 pink, 7 orange pull a ball out, put it back then pull another. Draw a tree diagram showing all possible outcomes Use your tree diagram to find the probability of getting: 2 pink 2 orange, A pink and an orange. B) The probability I have toast for breakfast is 0.6, the probability I will miss my bus is completely unrelated to my breakfast choice and is 0.2 What is the probability I will NOT: Have toast for breakfast Miss my bus Use your tree diagram to find the probability of: Having toast and missing my bus Not having toast and missing my bus Not having toast and not missing my bus C) I am tossing a coin and rolling a dice: Draw a tree diagram to show all possible outcomes. A head a 3 A tails and a number bigger than 4 A tails with a 3 or a heads with a 1 D) I have some songs on my mp3 player, 4 are rock, 7 are Pop and 11 are Hip Hop. I put my mp3 player on shuffle and listen to 2 songs (it is possible to listen to the same song twice in a row) Draw a tree diagram to show all the possible outcomes, Find the probability that I will listen to: Hip Hop then Pop Rock twice A Rock song and a pop song in any order 2 songs which are the same style (rock and rock or pop and pop ect.)

Tree diagrams 2 Dependant Events
What happens when one event affects the other? Tree diagrams 2 Dependant Events

I have a bag with 2 red and 8 green counters
I have a bag with 2 red and 8 green counters. I pick out a counter, don’t put it back, and pick another. Draw a tree diagram for this situation. Pick 1 Pick 2 R P(RR)=2/10x 1/9= 2/90 1/9 R G P(RG)=2/10x 8/9 = 16/90 8/9 2/10 8/90 P(GR)= 8/10 x 1/9= R 8/10 2/9 G P(G)= 8/10 x 7/0 = 56/90* G 7/9

Pick 1 Pick 2 What is the probability that I pick one of each? 32/90
If this happens I pick red then green OR green then red. When I see OR I know I have to add the probabilities So... P(RG) + P(GR) 16/90+16/90= 32/90 Pick 1 Pick 2 R P(RR)=2/10x 1/9= 2/90 1/9 R G P(RG)=2/10x 8/9 = 16/90 8/9 2/10 16/90 P(GR)= 8/10 x 2/9= R 8/10 2/9 G P(G)= 8/10 x 7/9 = 56/90 G 7/9

I have a bag of chocolates 12, they are white chocolate or dark chocolate. 7 of the chocolates are white chocolates. I pick one at random, eat it and pick another Draw a tree diagram for this situation. Pick 1 Pick 2 W P(WW)=7/12 X 6/11= 42/132 6/11 W D P(WD)=7/12 X 5/11= 35/132 5/11 7/12 P(DW)=5/12 X 7/11= 35/132 W 5/12 7/11 D P(DD)=5/12 X 4/11= 20/132 D 4/11

Pick 1 Pick 2 What is the probability that I have one of each?
If this happens I will have a white then dark OR a dark then white. When I see OR I know I have to add the probabilities So... P(WD) + P(DW) = 35/ /132= 70/132 or 35/66 Pick 1 Pick 2 W P(WW)=7/12 X 6/11= 42/132 6/11 W D P(WD)=7/12 X 5/11= 35/132 5/11 7/12 P(DW)=5/12 X 7/11= 35/132 W 5/12 7/11 D P(DD)=5/12 X 4/11= 20/132 D 4/11

Tree Diagrams 2 Answers: 4) 0.63 0.21 0.16 5) 90/380 24/380 48/390 190/380 132/390 Answers: 56/182 30/182 86/182 96/182 0.63 0.18 0.75 0.25 24/720 120/720 360/720 240/720 600/720 I have a bag of sweets, the sweets are toffees and fruit drops. There are 8 toffees and 6 fruit drops. I have a sweet at random then I my mate has one at random. Find the probability that: I have a toffee and my friend has a fruit drop We both have fruit drops We both have the same We end up with different sweets Alan is going to sit two exams, his performance is affected by his confidence. The probability he will pass the first exam is 0.7. If he passes the first exam the probability he passes the second is 0.9. If he fails the first exam the probability he will pass the second is 0.3. What is the probability that: a) He will pass both exams b) He won’t pass either exam c) He will only pass one exam 2. If I catch my bus on time the probability that I will be on time for work is 0.9, if I miss my bus the probability is 0.4. The probability that I will miss my bus is 0.3. Find the probability that: I will catch my bus and be on time I will miss my bus and be late I will be on time for work I will be late for work If have 20 counters in a bag, ten red, 6 blue and 4 yellow. I pick out a counter, don’t replace it, then I pick out another. What is the probability that I have: 2 reds No reds A yellow then a blue A yellow and a blue The second counter as red Both counters the same colour There are 10 pupils in my class, 4 boys and 6 girls. I need three of them to do a job for me. I select one pupil at a time at random, no pupil will be selected twice. What is the probability that the people doing the jobs will be: a) 3 boys b) 3 girls 1 boy and 2 girls What is the probability that: The second job will be done by a giirl? There will be at least 1 boy.

Probability - Find the probability of things NOT happening
10 multiple choice questions

1 out of 8 A) B) C) D) evens unlikely 7 out of 8 1 out of 8
If the Probability of an event happening is: 1 out of 8 What is the probability of the event NOT happening? evens unlikely A) B) 7 out of 8 1 out of 8 C) D)

3 out of 7 A) B) C) D) likely 4 out of 7 3 out of 7 7 out of 3
If the Probability of an event happening is: 3 out of 7 What is the probability of the event NOT happening? likely 4 out of 7 A) B) 3 out of 7 7 out of 3 C) D)

13 out of 20 A) B) C) D) 20 out of 13 unlikely 7 out of 10 7 out of 20
If the Probability of an event happening is: 13 out of 20 What is the probability of the event NOT happening? 20 out of 13 unlikely A) B) 7 out of 10 7 out of 20 C) D)

If the Probability of an event happening is:
0.2 What is the probability of the event NOT happening? 0.8 99.8 A) B) 0.18 0.2 C) D)

0.97 What is the probability of the event NOT happening? 0.03 0.13 A) B) 0.3 3 C) D)

10 multiple choice questions
Expected outcomes 10 multiple choice questions

I toss a coin 200 times, how many times would I expect to get a “head”?
1/2 50 A) B) 100 Even chance C) D)

I roll a coin 120 times, how many times do I expect to get a “3”?
30 20 A) B) 40 60 C) D)

I roll a dice 60 times how many times would I expect to get a number less than 4?
20 40 A) B) 60 30 C) D)

I roll a coin 360 times, how many times would I expect to get a number more than 4?
120 60 A) B) 180 300 C) D)

I roll a coin 180 times, how many times would I expect to get a prime number?
30 120 A) B) 60 90 C) D)

I roll a dice 240 times how many times would you expect to get a square number?
80 A) B) 120 160 C) D)

I probability that I will miss my bus is 2/7
I probability that I will miss my bus is 2/7. How many times do I expect to miss it in 2 weeks? 3 4 A) B) 2 8 C) D)

I probability that I will forget my keys is 3/5
I probability that I will forget my keys is 3/5. How many times do I expect to forget them over a period of 35 days? 15 14 A) B) 35 21 C) D)

I probability that I win when I play my friend at chess is 4/9
I probability that I win when I play my friend at chess is 4/9. How many times do I expect to loose if I play 27 games? 12 13 A) B) 15 9 C) D)

A) B) C) D) Probably Not Definitely Definitely Not Probably
I toss a coin 1000 times, I expect to get 500 tails and 500 heads, will I get that? Probably Not Definitely A) B) Definitely Not Probably C) D)

Mutually Exclusive Events
10 multiple choice questions

I play a game where the chance I win is 0
I play a game where the chance I win is 0.4, what is the probability I loose? (In this game we can’t draw) 0.4 0.5 A) B) 0.6 1 C) D)

I play a game where the chance I win is 0
I play a game where the chance I win is 0.35, what is the probability I loose? (In this game we can’t draw) 0.35 0.75 A) B) 0.5 0.65 C) D)

I play a game where the chance I win is 0. 4, the chance I draw is 0
I play a game where the chance I win is 0.4, the chance I draw is 0.3 what is the probability I loose? 0.4 0.3 A) B) 0.5 0.7 C) D)

I play a game where the chance I win is 0. 25, the chance I draw is 0
I play a game where the chance I win is 0.25, the chance I draw is 0.4 what is the probability I loose? 0.71 0.45 A) B) 0.81 0.35 C) D)

A) B) C) D) 0.4 0.6 0.3 0.5 Red Green Yellow Blue 0.3 0.1 0.2 ?
Some coloured balls are in a bag, the probability they will be pulled out are in the table. What is the probability a blue ball will be pulled out? Red Green Yellow Blue 0.3 0.1 0.2 ? 0.4 0.6 A) B) 0.3 0.5 C) D)

A) B) C) D) 0.47 0.2 0.53 0.02 Red Green Yellow Blue 0.3 0.25 ?
Some coloured balls are in a bag, the probability they will be pulled out are in the table. What is the probability a blue ball will be pulled out? Red Green Yellow Blue 0.3 0.25 ? 0.47 0.2 A) B) 0.53 0.02 C) D)

A) B) C) D) 0.1 0.001 0.0001 0.00001 Red Green Yellow Blue 0.9 0.09
Some coloured balls are in a bag, the probability they will be pulled out are in the table. What is the probability a blue ball will be pulled out? Red Green Yellow Blue 0.9 0.09 0.009 ? 0.1 0.001 A) B) 0.0001 C) D)

Dice Probability 10 multiple choice questions

If I roll a fair dice, what is the probability that I roll a...
6 6/6 1/6 A) B) 10/10 6/10 C) D)

2 1/2 2/6 A) B) 1/6 1/3 C) D)

Even number A) B) C) D) 1/6 1/3 2/6 1/2
If I roll a fair dice, what is the probability that I roll an.. Even number 1/6 1/3 A) B) 2/6 1/2 C) D)

7 6/6 A) B) 1/7 1/6 C) D)

2 or 3 2/12 1/3 A) B) 1/6 2/3 C) D)

Number more than 4? A) B) C) D) 3/6 1/2 4/6 1/3
If I roll a fair dice, what is the probability that I roll a... Number more than 4? 3/6 1/2 A) B) 4/6 1/3 C) D)

Factor of 12 5/6 2/3 A) B) 4/6 C) D)

Multiple of 3 A) B) C) D) 1/6 3/6 6/6 1/3
If I roll a fair dice, what is the probability that I roll a... Multiple of 3 1/6 3/6 A) B) 6/6 1/3 C) D)

Square number A) B) C) D) 1/6 1/2 1/3 2/3
If I roll a fair dice, what is the probability that I roll a... Square number 1/6 1/2 A) B) 1/3 2/3 C) D)

Prime number A) B) C) D) 2/3 1/2 1/6 1/3
If I roll a fair dice, what is the probability that I roll a... Prime number 2/3 1/2 A) B) 1/6 1/3 C) D)

The Probability Scale 10 multiple choice questions

A) B) C) D) Pick the word that would go here on a probability scale
Possible Probable A) B) Certain Very Likely C) D)

Maybe Likely A) B) Unlikely Even Chance C) D)

Very Unlikely Impossible A) B) Improbable Unlikely C) D)

Likely Certain A) B) Very Likely Nearly certain C) D)

Even chance Very Unlikely A) B) Likely Unlikely C) D)

Likely Very Likely A) B) Even Chance Impossible C) D)

Where would you put the probability of rolling a 7 on a normal dice?

Where would you put the probability of rolling an even number on a normal dice?

Where would you put the probability of rolling a 6 on a normal dice?

Where would you put the probability of rolling a number bigger than 1 on a normal dice?

Tree Diagrams 10 multiple choice questions

A) B) C) D) Dependant events Independent events Hours of fun
I toss a coin twice, this tree diagram can help me work out probabilities. Tossing one coin twice is an example of... H 1/2 1/2 H 1/2 T H 1/2 1/2 T 1/2 T Dependant events Independent events A) B) Hours of fun A bad referee C) D)

A) B) C) D) 2/2 1/4 1/2 2/4 What is the probability I toss two heads?

W I play a game where I win if I roll a 4 on a dice. I play the game twice. What probability goes in the blue boxes? W L W L L 5/6 1/6 A) B) 4/6 1/4 C) D)

W I play a game where I win if I roll a 4 on a dice. I play the game twice. What probability goes in the orange boxes? W L W L L 1/5 1/6 A) B) 4/6 5/6 C) D)

H 1/2 What is the probability the first coin is tails and the second is heads? 1/2 H 1/2 T H 1/2 1/2 T 1/2 T 1/4 2/4 A) B) 1/2 2/2 C) D)

W I play a game where I win if I roll a 4 on a dice. I play the game twice. What is the probability I will lose both games? 1/6 1/6 W 5/6 L W 1/6 5/6 L 5/6 L 10/12 5/36 A) B) 5/6 25/36 C) D)

W I play a game where I win if I roll a 4 on a dice. I play the game twice. What is the probability I win then lose? 1/6 1/6 W 5/6 L W 1/6 5/6 L 5/6 L 6/36 1/36 A) B) 6/12 5/36 C) D)

W I play a game where I win if I roll a 4 on a dice. I play the game twice. What is the probability I win one game and lose the other? 1/6 1/6 W 5/6 L W 1/6 5/6 L 5/6 L 5/36 10/36 A) B) 6/36 12/36 C) D)

W I play a game where I win if I roll a 4 on a dice. I play the game twice. What is the probability the results in both games is the same? 1/6 1/6 W 5/6 L W 1/6 5/6 L 5/6 L 25/36 27/36 A) B) 26/36 12/36 C) D)

W I play a game where the chance I win is 0.8. I play twice. What is the probability I win a game and lose a game?? 0.8 0.8 W 0.2 L W 0.8 0.2 L 0.2 L 0.32 0.16 A) B) 3.2 2 C) D)

Relative Frequency 10 multiple choice questions

A) B) C) D) W R W W What is relative frequency of getting a head?
I toss a biased coin 200 times I get these results: Frequency Heads 150 Tails 50 What is relative frequency of getting a head? W R A) B) W W C) D)

I toss a biased coin 200 times I get these results:
Frequency Heads 150 Tails 50 What is relative frequency of getting tails? 0.20 4 A) B) 0.50 0.25 C) D)

Frequency Heads 150 Tails 50 I toss the coin 500 times, how many times would I expect Heads? 375 400 A) B) 125 350 C) D)

I record all the different vehicles travelling down my road
I record all the different vehicles travelling down my road. Here are the results: Vehicle Frequency Car 10 Bike 6 Van 4 What is the probability that the next vehicle will be a car 0.5 10 A) B) 2 1 C) D)

I record all the different vehicles travelling down my road. Here are the results: Vehicle Frequency Car 10 Bike 6 Van 4 What is the probability that the next vehicle will be a bike 6 0.6 A) B) 0.3 0.60 C) D)

I record all the different vehicles travelling down my road. Here are the results: Vehicle Frequency Car 10 Bike 6 Van 4 What is the probability that the next vehicle will be a van 5 0.5 A) B) 0.4 0.2 C) D)

I record all the different vehicles travelling down my road. Here are the results: Vehicle Frequency Car 10 Bike 6 Van 4 If 80 vehicles pass by, how many would I expect to be cars? 20 40 A) B) 80 0.5 C) D)

I record all the different vehicles travelling down my road. Here are the results: Vehicle Frequency Car 10 Bike 6 Van 4 If 60 vehicles pass by, how many would I expect to be bikes? 10 1.8 A) B) 36 18 C) D)

I record all the different vehicles travelling down my road. Here are the results: Vehicle Frequency Car 10 Bike 6 Van 4 If 50 vehicles pass by, how many would I expect to be vans? 20 10 A) B) 8 12 C) D)

Frequency Heads 150 Tails 50 What is relative frequency of getting a head? 0.25 0.15 A) B) 0.75 1.5 C) D)

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