Ian Segment 5
We first calculate the probability that the two fair dice produce a prime. In the range 1~12, the possible primes are 2, 3, 5, 7, 11, and their probabilities are Now, since trials are independent of each other, probability that exactly 5 of the 10 recorded totals are prime follows a Binomial distribution with , then .
When , Binomial distribution approaches normal distribution with the same expectation and variance, so we have (A=500010000, B=500020000)
H=@(f) ceil((9-1000*log10(1-f))/(log10(1+2*f)-log10(1-f))); xaxis=[0.1:0.00001:0.2]; plot(xaxis,arrayfun(H,xaxis)) 1-binocdf(431,1000,0.5)