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Two goalkeeper Annie and paddy hit the ball to its destined basket in succession. Their probabilities of hitting by both of them correctly are 0.4 and 0.3 respectively. Paddy will only hit the ball only when Annie misses it. The probability that the ball will go to the destined basket by paddy is?

Two goalkeeper Annie and paddy hit the ball to its destined basket in succession. Their probabilities of hitting by both of them correctly are 0.4 and 0.3 respectively. Paddy will only hit the ball only when Annie misses it. The probability that the ball will go to the destined basket by paddy is? Correct Answer 0.31

⇒ Let the events, A = Annie hit the target, B = Paddy hit the target

⇒ Their corresponding probabilities are P(A) = 0.4 and P(B) = 0.3

⇒ P (A¯) = 0.6 and P (B¯) = 0.7

⇒ Required probability = P(A¯) P(B) + P (A¯) P (B¯) P (A¯) P(B) + ……

⇒ (0.6) × (0.3) + (0.6) × (0.7) × (0.6) × (0.3) + (0.6) × (0.7) × (0.6) × (0.7) × (0.6) × (0.3) + ……….

⇒ 0.18 ×

⇒ 0.18 ×

⇒ 0.18/0.58 = 0.310

∴ Answer is 0.310

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