Question

Consider rolling two fair six-sided dice.

a) Given that the roll resulted in sum of 8, find the conditional probability that first die roll is 6.

b) Given that the roll resulted in sum of 4 or less, find the conditional probability that doubles are rolled.

c) Given that the two dice land on different numbers, find the conditional probability that at least one die is a 6.

Answer 1

By  rolling two fair six-sided dice then possible outcomes

a) Favorable outcomes of that the roll resulted in sum of 8 are (2,6),(3,5),(4,4), (5,3), (6,2)

and favorable outcomes of the roll resulted in sum of 8 and first die roll is 6 are (6,2)

probability =

b) Favorable outcomes of that the roll resulted in sum of 4 or less are (1,1),(1,2),(1,3), (2,1), (2,2),(3,1)

and Favorable outcomes of that the roll resulted in sum of 4 or less and doubles are rolled is (1,1),(2,2)

Probability =

c) Number of favorable outcomes of the two dice land on different numbers are 30

and  Number of favorable outcomes of the two dice land on different numbers and  at least one die is a 6 are 5

Probability =