Problem 2 One hundred athletes are trying to qualify for the

Problem 2. One hundred athletes are trying to qualify for the finals. Each of them has to pass the preliminary stage and the advanced stage. Each athlete passes the preliminary stage with the probability 0.4 and the advanced stage with probability 0.7 independently. Each athlete passes stages independently of all other athletes. Let N be the number of people who pass the preliminary stage and fail to pass the advanced stage. Estimate the probability P(N

Solution

probability to pass the preliminary stage and fail to pass the advanced stage = 0.4*0.3 = 0.12

now N ~ Bin(100,0.12)

P(N<=15) = P(N=0)+P(N=1)+.........+P(N=15)

=0.8585511