The probability that A hits a target is `(1//3)` and the probability that B hits it is `(2//5)`. What is the probability that the target will be hit if both A and B shoot at it ?

The probability that A hits a target is `(1//3)` and the probability t

1.	The probability that A hits a target is `(1//3)` and the probability that B hits it is `(2//5)`. What is the probability that the target will be hit if both A and B shoot at it ?
Answer» Let `E_(1)=` event that A hits the target, and `E_(2) =` event that B hits the target. Then, `P(E_(1))=1/3` and `P(E_(2))=2/5`. Clearly, `E_(1)` and `E_(2)` are independent events. `:. P(E_(1) nn E_(2))=P(E_(1))xxP(E_(2))=(1/3xx2/5)=2/15`. `:.` P(target is hit) `=P` (A hits or B hits) `=P(E_(1) uu E_(2))` `=P (E_(1))+P (E_(2))-P (E_(1) nn E_(2))` `=(1/3+2/5-2/15)=9/15=3/5`. Hence, the required probability is `3/5`.

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The probability that A hits a target is `(1//3)` and the probability that B hits it is `(2//5)`. What is the probability that the target will be hit if both A and B shoot at it ?

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