Question

The probability that concert tickets are available by telephone is 0.93. For the same event, the probability that tickets are available through a Web site is 0.96. Assume that these two ways to buy tickets are independent. What is the probability that someone who tries to buy tickets both through the Internet and by the telephone will obtain at least one ticket? Round your answer to four decimal places.

Answer 1

The probability of obtaining at least one ticket either through the Internet or by telephone is approximately 99.72%, calculated by subtracting the combined probability of not getting a ticket by either method from 1.

Step-by-step explanation:

To find the probability that someone who tries to buy tickets both through the Internet and by the telephone will obtain at least one ticket, we need to understand the concept of independent events in probability. The key is to first calculate the probability of not getting a ticket through either method, and then subtract this value from 1 to find the probability of obtaining at least one ticket.

The probability of not getting a ticket by telephone is 1 - 0.93 = 0.07. Similarly, the probability of not getting a ticket through the Web site is 1 - 0.96 = 0.04. Since these events are independent, we can multiply these probabilities together to find the probability of not getting a ticket through either method: 0.07 * 0.04 = 0.0028.

To find the probability of getting at least one ticket, we subtract the probability of not getting any tickets from 1: 1 - 0.0028 = 0.9972. Therefore, the probability of obtaining at least one ticket is approximately 0.9972, or 99.72% when rounded to four decimal places