Question

Two dies are thrown simultaneously if x denote the numbers of sixes. Find the expectation of x   

kavya jain

Answer 1

Probability of a six for on one die : 1/6
probability of a non-six on one die : 5/6

The number of possibilities for two dies:

   0 number of sixes on both together:  5/6 * 5/6 = 25/36
   1 number of sixes from both together: 1/6* 5/6 + 1/6 * 5/6 = 10/36
   2 number of sixes from both together: 1/6 * 1/6 = 1/36

Sum of the above 3 probabilities is 1.

X = event that X sixes occur when two dies are thrown.

Expected value of X =  Summation  of  X * Probability of X
                         = 0 * 25/36 + 1 * 10/36 + 2 * 1/36 = 12/36 = 1/3