In a combat, A targets B, and both B and C target A. The probabilities of A, B, C hitting their targets are 2 / 3,1 / 2 and 1 / 3 respectively. They shoot simultaneously and A is hit. the probability that B hits his target whereas C does not

Question

In a combat, A targets B, and both B and C target A. The probabilities of A, B, C hitting their targets are 2 / 3,1 / 2 and 1 / 3 respectively. They shoot simultaneously and A is hit. the probability that B hits his target whereas C does not (A)  (1/2) (B) (1/3) (C) (1/4) (D) (1/6)

Tardigrade Admin · Accepted Answer

E1: A text targets B ; P(E1)=(2/3) E 2: B operatornametargets A ; P ( E 2)=(1/2) E 3: C text targets A ; P ( E 3)=(1/3) Given A is hit. Hence H 1: B hits A and C does not H 2: C hits A and B does not H 3: B and C both hit A ∴ P ( H 1)=(1/2) ⋅ (2/3)=(1/3) P ( H 2)=(1/3) ⋅ (1/2)=(1/6) P ( H 3)=(1/3) ⋅ (1/2)=(1/3) ⋅ (1/2) now, P ( H 1 / H 1 ∪ H 2 ∪ H 3)=((1/3)/(1)3+(1)6+(1/6)=(1/2)

Q. In a combat, A targets B, and both $B$ and $C$ target $A$ . The probabilities of A, B, C hitting their targets are $2/3, 1/2$ and $1/3$ respectively. They shoot simultaneously and $A$ is hit. the probability that $B$ hits his target whereas $C$ does not

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{6}$

Q. In a combat, A targets B, and both B and C target A. The probabilities of A, B, C hitting their targets are 2/3,1/2 and 1/3 respectively. They shoot simultaneously and A is hit. the probability that B hits his target whereas C does not

21​

31​

41​

61​

Q. In a combat, A targets B, and both $B$ and $C$ target $A$ . The probabilities of A, B, C hitting their targets are $2/3, 1/2$ and $1/3$ respectively. They shoot simultaneously and $A$ is hit. the probability that $B$ hits his target whereas $C$ does not

$\frac{1}{2}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{1}{6}$