Cristiano Ronaldo has a pass success percentage of 86% in the UEFA Champions Lea

Question

Cristiano Ronaldo has a pass success percentage of 86% in the UEFA Champions League. This measure summarizes the percentage of passes Ronaldo successfully made to his teammates instead of being intersected by the opponent. Ronaldo's coach has a strategy that in an indirect free kick, Ronaldo makes 2 passes before shooting at goal. Assuming Ronaldo's passes are independent, what is the probability Ronaldo successfully makes both passes in the first indirect free kick opportunity during the next game? A 0.1204 B 0.7396 C 0.8600 D cannot be determined

Explanation / Answer

A: Event of ronaldo Pass success

P(A) = Total number of passes successfully made by Ronaldo / Total number of passes made by Ronaldo = 86 /100 = 0.86

Probability of Ronaldoo successfully makes both the passes in the first indirect kick opportunity during the next game = Probability of making the first pass succssfully and making making the second pass successfully  in the first indirect kick opportunity during the next game = P( A and A)

Ronaldo passes are independent, i.e first event 'A' and the second event 'A' are independent.

Mulitplication theorem , if A and B are independent, then

P(A and B) = P(A) P(B)

so, P( A and A) = P(A)P(A) = 0.86 x 0.86 = 0.7396

Ans. B . 0.7396

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