Briyana Hall
11/19/23 8:17 PM
Question 5, 3.1.71
HW Score: $16 \%, 8$ of 50 points
Polnts: 0 of 5
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You are planning a three-day trip to Seattle, Washington, in October. Use the fact that on each day, it could either be sunny or rainy, and that each day is equally likely to be sunny or rainy to answer the following question.

What is the probability that it rains on exactly one day?
(Type an integer or a decimal. Do not round.)

Step 1 ：The problem is asking for the probability of a specific event in a sequence of independent events. In this case, the event is 'it rains' and the sequence is 'three days'. Each day can either be sunny or rainy, and each day is equally likely to be sunny or rainy. This is a binomial distribution problem, where we have 3 trials (days), each with 2 outcomes (sunny or rainy), and we want to find the probability of exactly 1 success (rainy day).

Step 2 ：The formula for the probability of k successes in n trials is: \(P(k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(C(n, k)\) is the binomial coefficient (the number of ways to choose k successes out of n trials), p is the probability of success on a single trial, and \((1-p)\) is the probability of failure on a single trial.

Step 3 ：In this case, n=3, k=1, and p=0.5 (since each day is equally likely to be sunny or rainy).

Step 4 ：Let's calculate this. n = 3, k = 1, p = 0.5, C = 3, P = 0.375

Step 5 ：The final answer is: The probability that it rains on exactly one day is \(\boxed{0.375}\).