SECTION 4.1 Probability Distributions 193 Verifying a Probability Distribution Verify that the distribution for the three-day forecast (see page 189) and the number of days of rain is a probability distribution. Days of rain, x 0 1 2 3 Probability, P1x2 0.216 0.432 0.288 0.064 SOLUTION If the distribution is a probability distribution, then (1) each probability is between 0 and 1, inclusive, and (2) the sum of all the probabilities equals 1. 1. Each probability is between 0 and 1. 2. ΣP1x2 = 0.216 + 0.432 + 0.288 + 0.064 = 1. Interpretation Because both conditions are met, the distribution is a probability distribution. TRY IT YOURSELF 3 Verify that the distribution you constructed in Try It Yourself 2 is a probability distribution. Answer: Page A38 Identifying Probability Distributions Determine whether each distribution is a probability distribution. Explain your reasoning. 1. x 5 6 7 8 P1x2 0.28 0.21 0.43 0.15 2. x 1 2 3 4 P1x2 1 2 1 4 5 4 -1 SOLUTION 1. Each probability is between 0 and 1, but the sum of all the probabilities is 1.07, which is greater than 1. The sum of all the probabilities in a probability distribution always equals 1. So, this distribution is not a probability distribution. 2. The sum of all the probabilities is equal to 1, but P132 and P142 are not between 0 and 1. Probabilities can never be negative or greater than 1. So, this distribution is not a probability distribution. TRY IT YOURSELF 4 Determine whether each distribution is a probability distribution. Explain your reasoning. 1. x 5 6 7 8 P1x2 1 16 5 8 1 4 1 16 2. x 1 2 3 4 P1x2 0.09 0.36 0.49 0.10 Answer: Page A38 EXAMPLE 3 EXAMPLE 4 Picturing the World A survey was conducted to determine how many credit cards people have.The results are shown in the histogram. (Adapted from YouGov Plc) Number Probability 0.05 0.10 0.15 0.20 0.25 0 1 2 3 4 5 6 or more/ do not know How Many Credit Cards Do You Have? P(x) x Estimate the probability that a randomly selected person has two or three credit cards.
RkJQdWJsaXNoZXIy NjM5ODQ=