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:
[tex]P(A\cup B) = P(A)+ P(B) - P(A\cap B)\\P(A\cup B) =0.21+0.28-0.15 = 0.34[/tex]
b) The probability that a wife will vote, given that her husband will vote is:
[tex]P(W|H)=\frac{P(H\cap W)}{P(H)}=\frac{0.15}{0.21} \\P(W|H)=0.7143[/tex]
c) The probability that a husband will vote, given that his wife will not vote (W') is:
[tex]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[/tex]
