Suppose the probability of remaining with a particular compa

Suppose the probability of remaining with a particular company 10 years or longer is 1/7. A man and a woman start work at the company on the same day.

What is the probability that both the man and the woman will work there less than 10 years? (Assume they are unrelated and their lengths of service are independent of each other.)

What is the probability that one or the other or both will work 10 years or longer?

Solution

Probability that both the man and the woman will work there less than 10 years

= Probability of man working for less than 10 years*Probability of woman working for less than 10 years

= (6/7)*(6/7) = 36/49 = 0.7347

probability that one or the other or both will work 10 years or longer

= 1 - Probability that both the man and the woman will work there less than 10 years

= 1-36/49

= 13/49 = 0.2653