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The probabilities of hitting a target by...

The probabilities of hitting a target by A, B and C are `3/5,3/4` and `1/3` respectively.
If all three hits the target simultaneously then find the probability of hitting the target by the least two of them.

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The correct Answer is:
N/a
Probability that A cannot hit the target `=1-3/5=2/5`
Probability that B cannot hit the target `=1-3/4=1/4`
Probability that C cannot hit the target `=1-1/3=2/3`
There are four ways in which at least two can hit the target.
(i) A,B andC can hit the target then its probability
`=3/5xx3/4xx1/3-9/60`
(ii) If A and B can hit the target and C cannot hit the target then its probability
`=3/5xx3/4xx2/3=18/60`
(iii) If A and C can hit the target and B cannot hit the target, then its probability
`=3/5xx1/4xx1/3=3/60`
(iv) If B and C can hit the target and A cannot hit the target, then its probability
`=2/5xx3/4xx1/3=6/60`
These four events are mutually exclusive therefore
The probability that at least two can hit the target
`=9/60+18/60+3/60+6/60=3/5`
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