Question

Two six sided dice are rolled and the two dice equals 7. what is the probability that one die is a 3

Answer 1

Let us solve the problem step by step.

here we have rolled two dice. So total no. of possible outcomes will be 6^2=36. These are (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6).

Now, among these cases the cases where the sum is seven for (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) i.e. there are 6 cases.

Now, it is time to calculate the probability.

The required probability is,

p = (No. of cases favorable for the event)/(Total no. of cases)

=6/36 = 1/6

Therefore your answer is 1/6.