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Question

A can hit a target 4 times in 5 shots. B 3 times in 4 shots and C twice in 3 shots. They fire a volley. What is the probability that two shots hit the target?

A
1330
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B
1730
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C
1130
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D
None of these
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Solution

The correct option is B 1330
Fire a volley means that A,BandC all try to hit the target simultaneously.

Two shots hit the target in one of the following ways:
(1) A and B hit and C fails to hit.
(2) A and C hit and B fails to hit.
(3) B and C hit and A fails to hit.

The chance of hitting by A,P(A)=45 and of not hitting by him P(A)=145=15.

The chance of hitting by B,P(B)=34 and of not hitting by him P(B)=134=14.

The chance of hitting by C,P(C)=23 and of not hitting by him P(C)=123=13.

The probability of (1) is P(ABC)=45×34×13=15.

The probability of (2) is P(ACB)=45×23×14=215.

The probability of (3) is P(BCA)=34×23×15=110.

Thus the probability that two shots hit the target is 15+215+110=1330.



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