A survey of couples in a city found the following probabilities:

The probability that the husband is employed is 0.85.

The probability that the wife is employed is 0.59.

The probability that both are employed is 0.50.

A couple is selected at random. Find the probability of the following.

(a) At least one of them is employed.

(b) Neither is employed.

Question

Keshawn Clayton

Mathematics

17 March, 00:14

A survey of couples in a city found the following probabilities:

The probability that the husband is employed is 0.85.

The probability that the wife is employed is 0.59.

The probability that both are employed is 0.50.

A couple is selected at random. Find the probability of the following.

(a) At least one of them is employed.

(b) Neither is employed.

+2

Answers (1)

Know the Answer?

Munchkin · Answer 1

Answer

(a) 0.94

(b) 0.06

Step-by-step explanation:

P (husband is employed) = P (H) = 0.85

P (wife is employed) = P (W) = 0.59

P (both are employed) = P (H∩W) = 0.50

(a) At least one of them is employed

= P (H∪W)

= P (H) + P (W) - P (H∩W)

=0.85 + 0.59 - 0.50

=0.94

(b) Neither is employed,

=1 - P (H∪W)

= 1-0.94

=0.06