 # Learning Target: I can… Find the probability of simple events.

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Learning Target: I can… Find the probability of simple events

Probability

How likely it is that an event will occur Zero probability is that something is sure NOT to happen Probability of 1 means that something is sure to happen Insurance companies use it to predict the likelihood that you will get into a car accident, burn your house down, etc. and decide if they want to insure you 01

How to write probability…

Review some basic probability What is the probability of… Spinning red Rolling a 3 Spinning orange or green Rolling a 1 or 4 Rolling an even number Spinning not yellow Drawing a queen in a deck of cards Drawing an ace or 7 in a deck of cards You try with a partner!! Probability of spinning purple? Probability of not spinning green Probability of spinning red or green or yellow Probability of rolling a six or two

1. When you have a number cube numbered 1-6, what is the probability of rolling a 1 or a 3? 2.When you have a number cube numbered 1-6, what is the probability of rolling an odd? 3.What is the probability of spinning a yellow or purple?

Learning Target: I can… Compare theoretical and experimental probability

How does the probability of spinning an even number change? 1.

If one “no prize” section is changed to pizza, how does the probability of winning a prize change? 1.

1. What is the theoretical probability of rolling a 6 on a die? 2.If you roll a die 90 times, how many times would you expect to roll a six? Theoretical Probability: ______________________________

1. What is the theoretical probability of rolling a number greater than 4 on a die? 2. If you roll a die 90 times, how many times would you expect to roll a number greater than 4?

3.Use the spinner to the right to answer the questions: What is the theoretical probability of landing on gray or pink? If you spin the spinner 120 times, how many times can you expect to land on gray or pink?

3.Use the spinner to the left to answer the questions: What is the theoretical probability of not landing on blue? If you spin the spinner 120 times, how many times can you expect to not land on blue

4.Tony has one blue shirt, two black shirts, four red shirts, and three yellow shirts. If Tony selects a random shirt, what is the probability he will pick a yellow shirt? If Tony does this for 30 days straight, how many days do you expect him to wear a yellow shirt?

4.Jack has three red and four black marbles in a bag. What is the theoretical probability that Jack will pick a black marble? If Jack repeats this process 56 times, how many times do you expect him to pick black?

1. Julie rolls a fair number cube is rolled 36 times. The results are shown at right. What is her experimental probability of rolling a 6? Experimental Probability: _________________________________

1. What is the experimental probability of rolling a 1?

2. What is the experimental probability of rolling an even number? How do the actual results compare to the number of times Julie would have expected to roll an even number?

2. What is the experimental probability of rolling a number less than 3? How do the actual results compare to the number of times Julie would have expected to roll a number less than 3?

3.At the fair, the spinner at right is spun 224 times. How many times do you expect to land on pizza? 4.Sixty people were awarded with pizza. How do the actual results differ from the expected results?

3.At the carnival, the spinner at left is spun 328 times. How many times do you expect to land on no prize? 4.One hundred sixty people were not awarded with a prize. How do the actual results differ from the expected results?

5.

A.Pizza was awarded 5 fewer times than expected B.Pizza was awarded 5 more times than expected C.The actual results do not differ from the expected results D.Pizza was awarded 45 times more than expected At the fair, the spinner was spun 320 times. The prize of pizza was awarded 85 times. How do the actual results differ from the expected results? EXIT

Learning Target: I can… Differentiate between experimental and theoretical probability

What is supposed to happen Example: P(flipping tails up) P(rolling a 4) P(spinning red) 1.Theoretical Probability

Brandon rolls a die 24 times. How many times can he expect to land on a six? Because 1/6 is his THEORETICAL PROBABILITY

Because the theoretical probability is 1/5

Suzie spins the spinner 72 times. How many times can she expect to land on red? a.18 b.10 c.288 d.1/4

Probability after a given number of experiments 2. Experimental Probability

Example: Theoretical probability of getting a heads is always ½ Paisley flipped a coin 114 times. How many times can you expect her to get heads? Paisley’s Experiment: H: 65T: 49 Experimental Probability:

Brandon rolls a die 24 times. How many times can he expect to land on a six? Because 1/6 is his THEORETICAL PROBABILITY When he does roll his results are as follows: 1: IIII 2: IIII 3: IIII 4: I 5: IIII II 6: II What is his EXPERIMENTAL PROBABILITY?

1) What is the theoretical probability of landing on yellow? 2) You spin 100 times, how many times do you expect to get yellow? 3) You spin 100 times and your results are as follows. What is your experimental probability of getting yellow? G: 30B: 29Y: 21R: 20

A class designed the spinner shown to award prizes at the school fair. At the fair, 450 students spun the spinner. The class awarded 115 slices of pizza, 49 CDs and 78 DVDs. How do the actual results differ from the expected results? A. The class awarded more CDs than expected. B. The class awarded fewer slices of pizza than expected. C. The class awarded more DVDs than expected. D. The actual results do not differ from the expected results.

EXIT

A.Pizza was awarded 5 fewer times than expected B.Pizza was awarded 5 more times than expected C.The actual results do not differ from the expected results D.Pizza was awarded 45 times more than expected At the fair, the spinner was spun 320 times. The prize of pizza was awarded 85 times. How do the actual results differ from the expected results? EXIT

Learning Target: I can… Find the probability of independent and dependent events

Independent Independent event-the first outcome does not affect the outcome of the second event –On a number cube, the outcome of rolling a 4 is not impacted by the outcome of spinning a green on a spinner

Independent or Dependent? P(spinning green, then yellow) P(spinning yellow twice in a row)

Independent or Dependent? P(green, then red) if the first is replaced P(green, then red) if the first is not replaced P(green, then green) if the first is replaced P(green, then green) if the first is not replaced

Independent or Dependent? There is a bag of 3 red marbles, 6 blue marbles, and 5 white marbles. What is the probability of drawing out a white marble and then a red marble without replacement?

Independent or Dependent? There is a bag of 3 red marbles, 6 blue marbles, and 5 white marbles. What is the probability of drawing out a white marble and then a red marble with replacement?

Level 4

Level 5

Level 6 1.Sarah draws four cards from a deck. She draws, then replaces, then draws again. Find the probability of drawing 4 aces. 2.Four cards are drawn from a deck without replacement of the previous draw. Find the probability of drawing 4 aces. 3.A coin is tossed five times. What is the probability that the coin will land tails up all five times?

Exit (2 red, 1 blue chip in bag) 1) Experiment #1: Draw a chip, put it back. Draw a chip again. What is P(red, then red)? 2) Experiment #2: Draw a chip, then draw another without replacing the first chip. What is P(red, then red)?

Check point 4. What is the probability of flipping a head then spinning yellow? 5. What is the probability of rolling a 4 then spinning not the color red? 6.What is the probability of rolling an even number and then orange? 7.BONUS: Flip a tail, roll an even, spin a red or green

Replacement-putting the item back or not??? If you have a bag of 3 red and 5 white marbles, what is the probability of drawing a red? What is the probability of drawing a red marble and not replace it in the bag then draw another red?

Dependent Dependent event- the outcome of the first event affects the outcome of the second event (no replacement) – Draw from a bag of 14 marbles (5 red and 9 green), and not put that marble back into the bag

Dependent Events: Without replacement BAG OF 5 RED AND 9 BLUE MARBLES What is the probability of drawing a red marble and you don’t put it back into the bag and then draw a blue? What is the probability of drawing a red marble and you don’t put it back into the bag and then draw another red in the bag?

Checkpoint 8. There is a bag of 3 red marbles, 6 blue marbles, and 5 white marbles. What is the probability of drawing out a white marble and then a red marble without replacement? 9. There is a bag of 3 red marbles, 6 blue marbles, and 5 white marbles. What is the probability of drawing out a white marble and then a red marble with replacement?

Checkpoint #10

Check Point answers (1-10) 1. When you have a number cube numbered 1-6, what is the probability of rolling a 1 or a 3? 2.When you have a number cube numbered 1-6, what is the probability of rolling an odd? 3.What is the probability of spinning a yellow or purple?

4. What is the probability of flipping a head then spinning yellow? 5. What is the probability of rolling a 4 then spinning not the color red? 6.What is the probability of rolling an even number and then orange? 7.BONUS: Flip a tail, roll an even, spin a red or green

8. There is a bag of 3 red marbles, 6 blue marbles, and 5 white marbles. What is the probability of drawing out a white marble and then a red marble without replacement? 9. There is a bag of 3 red marbles, 6 blue marbles, and 5 white marbles. What is the probability of drawing out a white marble and then a red marble without replacement?

#10

homework When you see: P (green, 3) It means what is the Probability of spinning a green, then rolling a 3

Tree Diagram explains the shortcut Spinning a red is 1/5, then to spin an orange is another 1/5 So it is a 1/25 chance to spin a red, then orange SHORTCUT – multiply the 2 fractions 1/5 x 1/5 = 1/25 Let’s try some more together…

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