Three people A, B, C throw darts at a Dartboard during a pub game. Person A...

 

 

 

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Three people A, B, C throw darts at a Dartboard during a pub game. Person A has a hit probability pA = 0:3, i.e., for each throw, g applies that A hits the board with probability 30%. For person B g applies to hit probability pB = 0.2 and for C is still pc = 0.1. A throws nA = 10 times, B throws nB = 15 times and C rolls nC = 20 times. All castes are assumed to be independent. (a) Determine a (complicated) expression that contains summation signs, binomial coefficients, etc., and that specifies the exact probability that exactly k hits of the board occur during the evening. (b) Determine with the Central Limit Theorem (CLT) an approximate normal distribution for the number of hits of the dartboard. Determine from this an approximation of the probability that at least 12 hits occur. Three people A, B, C throw darts at a Dartboard during a pub game. Person A has a hit probability pA = 0:3, i.e., for each throw, g applies that A hits the board with probability 30%. For person B g applies to hit probability pB = 0.2 and for C is still pc = 0.1. A throws nA = 10 times, B throws nB = 15 times and C rolls nC = 20 times. All castes are assumed to be independent. (a) Determine a (complicated) expression that contains summation signs, binomial coefficients, etc., and that specifies the exact probability that exactly k hits of the board occur during the evening. (b) Determine with the Central Limit Theorem (CLT) an approximate normal distribution for the number of hits of the dartboard. Determine from this an approximation of the probability that at least 12 hits occur.