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Question

A, B, C are aiming to shoot a balloon, A will succeed 4 times out of 5 attempts. The chance of B to shoot the balloon is 3 out of 4 and that of C is 2 out of 3. If the three aim the balloon simultaneously, then find the probability that atleast two of them hit the balloon.

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Solution

P(A)=45, P(B)=34, P(C)=23
Chance of any two of these hitting the balloon is -
=P(A).P(B).P(¯C)+P(A)P(¯B)P(C)+P(¯A).P(B).P(C)

=45×34×13+45×14×23+15×34×23

=15+220+110

=4+2+220

=820

=25.
Hence, the answer is 25.


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