Probability 3 Question 35
35. $A$ is targeting to $B, B$ and $C$ are targeting to $A$. Probability of hitting the target by $A, B$ and $C$ are $\frac{2}{3}, \frac{1}{2}$ and $\frac{1}{3}$, respectively. If $A$ is hit, then find the probability that $B$ hits the target and $C$ does not.
(2003, 2M)
Show Answer
Solution:
- Given, $P(A)=$ probability that $A$ will hit $B=\frac{2}{3}$
$P(B)=$ probability that $B$ will hit $A=\frac{1}{2}$
$P(C)=$ probability that $C$ will hit $A=\frac{1}{3}$
$P(E)=$ probability that $A$ will be hit
$$ \Rightarrow \quad P(E)=1-P(\bar{B}) \cdot P(\bar{C})=1-\frac{1}{2} \cdot \frac{2}{3}=\frac{2}{3} $$
Probability if $A$ is hit by $B$ and not by $C$
$$ =P(B \cap \bar{C} / E)=\frac{P(B) \cdot P(\bar{C})}{P(E)}=\frac{\frac{1}{2} \cdot \frac{2}{3}}{\frac{2}{3}}=\frac{1}{2} $$
