Question

Problem 5 Among married couples, 20% of the husbands (H) and 8% of the wives (W) watch Super Bowl. It is also known that the probability that at least one spouse of a married couple will be watching a Super Bowl is 0.23. A married couple is selected at random during a Super Bowl.

(b) What is the probability that both husband and wife are watching the Super Bowl?

Answer 1

Given that, Among married couples, 20% of the husbands (H) and 8% of the wives (W) watch Super Bowl.

P(H) = 0.20 and P(W) = 0.08

and probability that at least one spouse of a married couple will be watching a Super Bowl is 0.23.

That is, P(H or W) = 0.23

b) We want to find, P(H and W)

We know,

P(H or W) = P(H) + P(W) - P(H and W)

=> 0.23 = 0.20 + 0.08 - P(H and W)

=> 0.23 = 0.28 - P(H and W)

=> P(H and W) = 0.28 - 0.23

=> P(H and W) = 0.05

Therefore, the probability that both husband and wife are watching the Super Bowl is 0.05