Explanation
Let P(A),P(B), and P(C) be the probabilities of A, B, and C hitting their respective targets.
P(A)=32
P(B)=21⟹P(B′)=1−21=21
P(C)=31⟹P(C′)=1−31=32
A is hit if either B hits, C hits, or both hit.
P(A is hit)=1−P(B misses and C misses)
P(A is hit)=1−(P(B′)×P(C′))
P(A is hit)=1−(21×32)
P(A is hit)=1−31=32
We need to find the conditional probability that B hit and C did not, given that A was hit:
P(B∩C′∣A is hit)=P(A is hit)P(B∩C′)
Since B and C are independent:
P(B∩C′)=P(B)×P(C′)=21×32=31
Required Probability:
P=2/31/3
P=21
Correct Option: (a)
