Question

A game is played where players take turns rolling two six-sided dice, each with sides numbered 1-6. The numbers on the two dice are added together for each player's score. If the first player rolls a sum of 10, what is the probability that the second player rolls a HIGHER total?

Answer 1

`(1)/(12)`

Explanation:

Total number of possible outcomes when a dice is rolled six times

`= 6*6\\= 36`

Number of possible outcomes than have a sum greater than 10 are

`(6,5)\\(5,6)\\(6,6)\\`

Probability that the second player rolls a total higher than 10 is equal to the total number of possible outcomes with sum greater than 10 divided by total outcomes

`(3)/(36) \\= (1)/(12)`