AP EAMCET · Maths · Probability

Bill and George go target shooting together. Both shoot at a target at the same time. Suppose Bill hits the target with probability 0.7 where as George, independently, hits the target with probability 0.4. Given that exactly one shot hit the target, what is the probability that it was George's shot?

A \(\frac{2}{3}\)
B \(\frac{2}{9}\)
C \(\frac{1}{9}\)
D \(\frac{8}{9}\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{2}{9}\)

Step-by-step Solution

Detailed explanation

Let the probability, Bill hits the target is \(P(B)=0.7\), and similarly, probability that George hits the target is \(P(G)=0.4\) \(\because\) Events \(B\) and \(G\) are independent So, \(P(B \cap G)=P(B) P(G)=0.28\) \(\therefore\) The probability that George shot when it is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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