Each of three football players will attempt to kick a fieldgoal from the 25 yard

Question

Each of three football players will attempt to kick a fieldgoal from the 25 yard line. Ai denote the event that the field goalis made by player i. i=1,2,3. Assume that A1, A2 ,A3 aremutually independent and that P(A1) = .5, P(A2) = .7, P(A3)=.6 a) Compute the probability that exactly one player issuccessful. b) Compute the probability that exactly two players make afield goal (ie., one misses) Thank you for your time!! Each of three football players will attempt to kick a fieldgoal from the 25 yard line. Ai denote the event that the field goalis made by player i. i=1,2,3. Assume that A1, A2 ,A3 aremutually independent and that P(A1) = .5, P(A2) = .7, P(A3)=.6 a) Compute the probability that exactly one player issuccessful. b) Compute the probability that exactly two players make afield goal (ie., one misses) Thank you for your time!!

Explanation / Answer

One player successful = Probability just A1 is successful +Probability just A2 is successful + Probability just A3 issuccessful Since just A1 is successful only if the other two fail, this firstterm has probability = .5 * (1-.7) * (1-.6) One player successful = .5 * (1-.7) * (1-.6) + .7 (1-.5) (1-.6) +.6 (1-.5)(1-.7) = .29 Exactly two players successful is the same as exactly one playermissing... One player fails = Probability just A1 fails + Probability just A2fails + Probability just A3 fails = (1-.5)*.6*.7 + (1-.7)*.5*.6+(1-.6) * .5 * .7 = .44

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