A missile was fired at a plane where there are two targets, T1 and T2. If the probability ofhitting the targets T1 and T2 are a1 and a2 respectively, then find the probability that T1 was hit, ifit is known that T2 was not hit.
Question
A missile was fired at a plane where there are two targets, T1 and T2. If the probability ofhitting the targets T1 and T2 are a1 and a2 respectively, then find the probability that T1 was hit, ifit is known that T2 was not hit.
Solution
To solve this problem, we need to use the concept of conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred. If the event of interest is A and event B is known or assumed to have occurred, the conditional probability of A given B is usually written as P(A | B).
In this case, we want to find the probability that T1 was hit given that T2 was not hit. We can write this as P(T1 | not T2).
We know the individual probabilities of hitting T1 and T2, which are a1 and a2 respectively. However, we don't know the relationship between these two events. Are they independent? Are they mutually exclusive? Without this information, we can't calculate the exact probability.
If T1 and T2 are independent, then the probability of hitting T1 is not affected by whether T2 was hit or not. So, P(T1 | not T2) = a1.
If T1 and T2 are mutually exclusive, then the missile can't hit both targets. If T2 was not hit, then T1 must have been hit. So, P(T1 | not T2) = 1.
In any other case, we need more information to calculate the probability.
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