GOAL 1 FINDING THE PROBABILITY OF AN EVENT 2.8 Probability and Odds VOCABULARY probability of an event outcomes event theoretical probability favorable outcomes experimental probability EXAMPLE 1

Theoretical Probability and Experimental Probability Although these are technically different, the way we find each type of probability is similar. In other words:

Extra Example 1 a. You have 2 red and 2 black socks in a drawer. You reach in and pick two without looking. What is the probability P that they do not match? A picture can help solve this. Determine if each outcome is favorable or unfavorable. Unfavorable Favorable Unfavorable Note: We will write probabilities as decimal numbers.

Extra Example 1 (cont.) EXAMPLE 2 b. In a group of students, 12 ride the bus to school, 8 are driven to school, and 5 walk. One of the students is chosen at random from the group. What is the probability P that the student walks to school? First, determine the number of favorable outcomes and the number of possible outcomes. Favorable outcomes = 5, Possible outcomes = 25 Use the equation for probability.

Extra Example 2 Use the circle graph below showing the responses of 250 college students to a survey asking “Which factor is most likely to influence your job choice after graduation?” If you were to ask a randomly chosen college student this question, what is the experimental probability that the student would say “type of company”?

Checkpoint Last January it snowed 7 days, was sunny 18 days, and was cloudy 6 days. a.Based on this information, what is the probability that it will snow on a randomly chosen day in January? b. Is the probability in part (a) experimental or theoretical? Experimental

GOAL 2 FINDING THE ODDS OF AN EVENT Although similar, finding the odds that an event will occur is slightly different than finding the probability it will occur. 2.8 Probability and Odds

So how are unfavorable outcomes, favorable outcomes, and possible outcomes related? Possible outcomes = unfavorable + favorable This means that if we know two of these, we can find the third: Favorable outcomes = possible - unfavorable Unfavorable outcomes = possible - favorable EXAMPLE 3

Extra Example 3 You randomly choose a letter from the word SUMMER. What are the odds that the letter is a vowel? First, determine the number of favorable and unfavorable outcomes. Favorable (U, E): 2 Unfavorable (S, M, M, R): 4 Then use the equation for odds. Note: Odds are not written as a decimal, but as a ratio of two numbers using “to.”

How are probability and odds related? You can think of it in two ways: EXAMPLE 4

Extra Example 4 The probability that a randomly chosen 4 digit security code contains at least one zero is What are the odds that a 4 digit security code contains at least one zero? Since we know the probability the code contains at least one zero, we use the following formula and then substitute and simplify.

Checkpoint 1. A candy dish contains 12 miniature chocolate bars and 21 hard candies. What are the odds that a candy picked at random from the dish will be a hard candy? 2. In a shoe factory, the probability of a defective shoe being produced is What are the odds of producing a defective shoe? 7 to 4 1 to 199

QUESTIONS?