(1) Each of three football players willattempt to kick a field goal from the 25-

Question

   (1) Each of three football players willattempt to kick a field goal from the 25-yard line. Let Ai denotethe event that the field goal is made by player i, i = 1,2,3.Assume that A1,A2,A3 are mutually independent and that P(A1) = 0.5,P(A2) = 0.7, and P(A3) = 0.6.    (a) Compute the probability that exactly oneplayer is successful.    (b) Compute the probability that exactly twoplayers make a field goal (i.e., one misses).       (1) Each of three football players willattempt to kick a field goal from the 25-yard line. Let Ai denotethe event that the field goal is made by player i, i = 1,2,3.Assume that A1,A2,A3 are mutually independent and that P(A1) = 0.5,P(A2) = 0.7, and P(A3) = 0.6.    (a) Compute the probability that exactly oneplayer is successful.    (b) Compute the probability that exactly twoplayers make a field goal (i.e., one misses).   

Explanation / Answer

For this problem: P(A1') = Player 1 misses = .5 P(A2') = Player 2 misses = .3 P (A3') = Player 3 misses = .4 a.) the probability that exactly one player is successful: P(A1)*P(A2')*P(A3') + P(A1')*P(A2)*P(A3') + P(A1')*P(A2')*P(A3) = .5*.3*.4 + .5*.7*.4 + .5*.3*.6 = .06 + .14 + .09 =.29

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