Question

An actress has a probability of getting offered a job after a try-out of 0.13. She plans to keep trying out for new jobs until she gets offered. Assume outcomes of try-outs are independent.

Find the probability she will need to attend more than 7 try-outs

Answer 1

To find the probability that the actress will need to attend more than 7 try-outs before getting offered a job, we can use the geometric distribution. Using the formula P(X > x) = (1 - p)^x, where x is the number of try-outs, the probability is 0.643.

Step-by-step explanation:

To find the probability that the actress will need to attend more than 7 try-outs before getting offered a job, we can use the concept of a geometric distribution. The geometric distribution models the number of independent trials needed to achieve a success (in this case, getting offered a job).

The probability of success in one trial is given as 0.13. The probability of needing to attend more than 7 try-outs is equal to the sum of the probabilities of needing 8, 9, 10, and so on try-outs.

To calculate these probabilities, we can use the formula:

P(X > x) = (1 - p)^x, where x is the number of try-outs.

Substituting the given value of p = 0.13, the probability of needing to attend more than 7 try-outs is:

P(X > 7) = (1 - 0.13)^7 = 0.643