Question

The probability that your call to a service line is answered in less than 30 seconds is 0.64. Assume that your calls to this service line are independent. What is the probability that out of 5 calls, at least 3 calls are answered in less than 30 seconds?

Answer 1

To find the probability that at least 3 out of 5 calls are answered in less than 30 seconds, use the binomial probability formula for 3, 4, and 5 successful calls and sum the probabilities.

Step-by-step explanation:

The probability that out of 5 independent calls to a service line, at least 3 are answered in less than 30 seconds can be solved using the binomial probability formula. In this case, the probability of success (a call being answered in less than 30 seconds) is 0.64. The question asks for the probability of getting at least 3 successes out of 5 trials, which means we need to calculate the probabilities for 3, 4, and 5 successful calls and sum them up.

The binomial probability of exactly k successes in n trials is calculated as P(X=k) = (n choose k) × (p^k) × ((1-p)^(n-k)), where (n choose k) is the binomial coefficient, p is the probability of success, and k is the number of successes.

Using this formula, we calculate each of the probabilities for getting exactly 3, 4, and 5 successful calls, and then sum them to get the final probability for at least 3 successful calls out of 5.