Assume that 5 people, including the husband and wife pair, apply for 2 sales positions. People are hired at random.

Question

Assume that 5 people, including the husband and wife pair, apply for 2 sales positions. People are hired at random.

(1) What is the probability that both the husband and wife are hired? 

 

(2) What is the probability that one is hired and one is not?

Answer 1

There are always so many ways of answering problems like this.

1) The husband and wife are one pair and, as there are 5 people total, there are C(5,2) = 10 pairs.

P(husband and wife selected) = 1/10

2) P(selecting one and not the other) = 1 - P(selecting neither, or 2 of the other 3) - P(selecting both) =

1 - C(3,2)/10 - 1/10 = 1 - 3/10 - 1/10 = 6/10 = 3/5

Another way: P(selecting the husband and one of the 3 not the wife) + P(selecting the wife and one of the 3 not the husband) = 3/10 + 3/10 = 6/10 = 3/5