8.7 – Probability. Probability Probability = the likelihood that an event will occur Outcomes = possible results of an event Probability formula: P(event)

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Presentation transcript:

8.7 – Probability

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).

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

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 =

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

Find the probability that the sum of 3 rolled dice is / / / / /108

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/ / / /3

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/ / /4 5. 5/18

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

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%

Find the probability of drawing a 10 or a 6 from a standard deck. 1. 1/ / / / /52

Find the probability of drawing a diamond or a non-ace from a standard deck / / / / /4