1. Probability

2. Probability vs. Statistics
Probability is a prediction of how likely an event could happen
Statistics is a calculated result of an event happening

3. Probability Number of ways that event can happen
Probability of an event happening =
Total number of possible outcomes
Number of ways that event can happen
Probability of an event happening =
Total number of possible outcomes
Number of “correct” outcomes

4. Probability Different ways to express probability
Fraction, decimal, %, ___ in/out of _____
1/10
0.10
10%
1 in 10
1 out of 10

5. What does is mean?
A probability of 1 means the event is certain to happen.
A probability of 0 means the event can’t happen. It’s not possible.
A probability above 0.5 (50%) means it is likely to happen.
A probability less than 0.5 (50%) means it is not likely to happen.

6. Examples
In a bag there are 20 marbles. There are 4 blue, 6 red, 2 green, and 8 yellow.
What is the probability of drawing a blue marble?
What is the probability of drawing a red marble?
4 20 = 1 5 = 0.2 = 20%
6 20 = = 0.3 = 30%

7. Dice
A standard 6-sided die has dots representing the numbers 1-6 on its 6 sides
Each side has an equal chance of rolling face up

8. Playing Cards A standard deck of playing cards has 52 cards
4 suits – Diamonds, Hearts, Spades , Clubs
13 cards in each suit – Ace, 2-10, Jack, Queen, King
Face cards – Jack, Queen, King

9. Playing Cards

10. More Examples
1 2
What is the probability of flipping a “fair coin” and getting tails?
What is the probability of rolling a 6-sided die and getting a 5?
What is the probability of drawing an ace from a standard deck of playing cards?
1 6
4 52 = 1 13

12. OR 2 6 What is the probability of rolling a die and getting a 1 OR 6?
Total outcomes
“correct” outcomes
2 6

13. OR
2 6
What is the probability of rolling a die and getting a 1 OR 6?
Probability of just the 1?
Probability of just the 6?
How do these answers compare?
Add the probabilities of each individual event together
1 6
1 6
1 6
1 6
2 6 + =

14. Adding Fractions
When adding fractions, the bottoms(denominator) have to be the same
Add the tops (Numerator)
1 2
1 3 + =
3 6
2 6
5 6 + =

15. Table Diagram H T H T HH HT TT
Possible outcomes for flipping 2 coins together H T HH HT TT H T

17. AND
What is the probability of flipping 2 coins and getting 2 tails?
Probability =
Total outcomes
“correct” outcomes
1 4

18. AND
1 4
What is the probability of flipping 2 coins and getting 2 tails?
Probability of 1st coin being tails?
Probability of 2nd coin being tails?
How do these answers compare?
Multiply the probabilities of each individual event together
1 2
1 2
1 2
1 2
1 4 x =

19. Multiplying Fractions
When multiplying fractions, the bottoms(denominator) DO NOT have to be the same
Multiply across the top (Numerator)
Multiply across the bottom (Denominator)
1 2
1 4
1 8 x =

20. Tree Diagrams H H T H H T T H H T T H T T HHH HHT HTH HTT THH THT TTH
1st Coin
2nd Coin
TTT
3rd Coin

22. Dependent Events Probability is affected by previous events
Drawing a marble out of a bag, if the marble is not replaced, the number of marbles left in the bag is different
Probability changes now that there is a different number of marbles

23. Examples
In a bag there are 20 marbles. There are 4 blue, 6 red, 2 green, and 8 yellow.
What is the probability of drawing two blue marbles?
4 20 𝑥 3 19 = = 4 95