A pair of unbiased dice are rolled 45 times What is the prob

A pair of unbiased dice are rolled 45 times. What is the probability that a 6 will appear 25 times?

Solution

two dice roll,          n = 2 , p = 1/ 6

The probaility of 6 up is

        P ( x; 2, 1/6) = [ 2 ! / x! ( 2 - x )! ] ( 1/ 6 ) ^x ( 5 / 6 )^2-x

mean

<x > = 2 / 6   = 0.333

standard deviation

      sigma = sqrt ( 2 (1/ 6 ) ( 5 /6 )) = 0.196

Distribution is not symmetric, the most probability is 1