SATHEE: Probability 3 Question 35

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)

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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

$\Rightarrow P (E) = 1 - P (\bar{B}) \cdot P (\bar{C}) = 1 - \frac{1}{2} \cdot \frac{2}{3} = \frac{2}{3}$

Probability if $A$ is hit by $B$ and not by $C$

$= P (B \cap \bar{C} / E) = \frac{P (B) \cdot P (\bar{C})}{P (E)} = \frac{\frac{1}{2} \cdot \frac{2}{3}}{\frac{2}{3}} = \frac{1}{2}$

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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 23,12 and 13, respectively. If A is hit, then find the probability that B hits the target and C does not.

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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.