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.

Question

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.

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Answer 1

Bot GPT 3.5 answered
30 days ago

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.