A recent survey showed that 71 full-time employees out of a sample of 500 did not use all of their vacation days last year. However, 86 of those studied expressed a desire for more vacation time. Based on this sample, if a full-time employee is chosen at random, what is the probability that he or she is content with the vacation allowance? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Answer 1

First, we need to calculate the number of employees who are content with the vacation allowance.

Number of employees who did not use all vacation days last year: 71
Number of employees who desire more vacation time: 86

Number of employees content with vacation allowance: 500 - 71 - 86 = 343

Probability of choosing an employee who is content with the vacation allowance:
343/500 = 0.686

Therefore, the probability that a full-time employee chosen at random is content with the vacation allowance is 0.686.