Question

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 1

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`.