Question

2.82 For married couples living in a certain suburb, the probability that the husband will vote on a bond referendum is 0.21, the probability that the wife will vote on the referendum is 0.28, and the probability that both the husband and the wife will vote is 0.15. What is the probability that (a) at least one member of a married couple will vote? (b) a wife will vote, given that her husband will vote? (c) a husband will vote, given that his wife will not vote?

Answer 1

Answer:

a) 0.3400

b) 0.7143

c) 0.0833

Step-by-step explanation:

Let H be the event that the husband will vote on the bond referendum, and W be the event that the wife will vote on the bond referendum.

P(H) = 0.21

P(W) = 0.28

P(H and W) = 0.15

a) The probability that at least one member of the couple will vote is:

$P(A\cup B) = P(A)+ P(B) - P(A\cap B)\\P(A\cup B) =0.21+0.28-0.15 = 0.34$

b) The probability that a wife will vote, given that her husband will vote is:

$P(W|H)=\frac{P(H\cap W)}{P(H)}=\frac{0.15}{0.21} \\P(W|H)=0.7143$

c) The probability that a husband will vote, given that his wife will not vote (W') is:

$P(H|W')=\frac{P(H) -P(H\cap W)}{1-P(W)}=\frac{0.21-0.15}{1-0.28} \\P(H|W')=0.0833$