A pair of fair dice one red and one white two times a What i

A pair of fair dice, one red and one white, two times.

a) What is the probability that each die shows the same value on the second roll as on the first roll?

b) What is the probability that the sum of the two dice is the same on both rolls?

c) What is the probability that the sum of the two dice is greater on the second roll?

Solution

a)If you roll a pair (1-1, 2-2, 3-3, 4-4, 5-5, 6-6...six combinations) on the first roll, then you have a 1/36 chance of rolling that same pair again on the second roll.

If you roll a non-pair (30 different combinations) on the first roll, then you have a 2/36 chance of rolling the same combo again. For example, if you roll a 2 3 on the first roll, you can roll a 2 3 or a 3 2 on the second roll.

So...
6/36 x 1/36 = 6/1296 = P(rolling a pair twice in a row)
30/36 x 2/36 = 60/1296 = P(rolling a non pair twice in a row)

Adding them up, you get
66/1296 = 11/216 = 5.09%

b)P(both sum the same)
= [ 2(1^2 + 2^2 + 3^2 + 4^2 + 5^2) + 6^2 ] / 6^4
= [ 2*55 + 36 ] / 1296
= 146 / 1296
= 73 / 648

c)