Two policemen A and B fire once each simultaneously at an escaping convict. P(A hits) = 3×P(B hits). P(convict not injured) = 0.5. The probability that B hits the convict is:
Options:
(A) 0.14
(B) 0.22
(C) 0.33
(D) 0.40
Official Answer Key:
A
Step-by-Step Solution & Explanation
Let P(B hits)=p, P(A hits)=3p. P(neither hits) = (1-3p)(1-p) = 0.5. Expand: 1-4p+3p²=0.5 ⟹ 3p²-4p+0.5=0 ⟹ p = [4±√(16-6)]/6 = [4±3.162]/6. Taking the physically valid root (p<1/3 so that 3p≤1): p = (4-3.162)/6 = 0.838/6 = 0.14. Answer: A.
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