1. 8.7 – Probability

2. Probability Probability = the likelihood that an event will occur Outcomes = possible results of an event Probability formula: P(event) = # favorable outcomes # possible outcomes All probabilities range from zero (impossible) to one (guaranteed).

3. Ex: Find the probability of rolling 2 dice and receiving a total of 5. There are a total of 6 outcomes on each die, so the total amount of outcomes for 2 dice is 66= 36 It may help to write outcomes in a sample space… Of those outcomes, how many add to 5? (1, 4), (2, 3), (3, 2), (4, 1) So the probability is 4/36, which reduces to 1/9

4. Ex: You are playing poker with a friend, so you are dealt 5 cards. What is the probability of getting 2 aces and 3 non-aces? Total possible poker hands: Total possibilities of 2 aces and 3 non-aces: Probability =

5. Find the probability that the sum of 2 rolled dice is 8. 1. 1/36 2. 1/9 3. ½ 4. 5/36 5. 2/9

6. Find the probability that the sum of 3 rolled dice is 17. 1. 1/72 2. 1/216 3. 17/216 4. 5/216 5. 1/108

7. In a bag of 3 green marbles, 2 blue marbles, and 5 red marbles, what is the prob. of picking a green or a blue marble? 1. 1/2 2. 3/50 3. 1/15 4. 3/10 5. 1/3

8. In a bag of 3 green marbles, 2 blue marbles, and 5 red marbles, what is the prob. of picking a green or a blue, then a red, without replacement? 1. 1/3 2. 1/24 3. 3/100 4. 1/4 5. 5/18

9. If A and B are events in the same sample space, then the probability of A or B occurring is given by: P(A U B) is the probability of A or B occurring and is called A “union” B is the probability of A and B occurring simultaneously and is called A “intersection” B Ex: One card is selected randomly from a standard 52-card deck. What is the probability that it is a heart or a jack? There are 13 hearts in a deck and 4 jacks, and 1 jack of hearts

10. If A represents the desirable outcomes in a sample space, its complement, or A’, represents the undesirable outcomes in the sample space. P(A’) = 1 – P(A) Ex: The probability of Mr. Werner touching the net of a basketball hoop is 4%. What is the probability that he doesn’t touch the net? 100% - 4% = 96%

11. Find the probability of drawing a 10 or a 6 from a standard deck. 1. 1/169 2. 2/13 3. 7/52 4. 4/13 5. 15/52

12. Find the probability of drawing a diamond or a non-ace from a standard deck. 1. 49/52 2. 4/13 3. 10/13 4. 15/13 5. 1/4