Please Help! Two standard dice are rolled.

Question

Two standard dice are rolled.

1. a) What is the probability of rolling a pair (both the same number)?

d) What is the probability that a sum less than 7 is not rolled?

Answer 1

There are 36 possible outcomes ( 1,1 ) (1,2) (1,3) .... (6,6)

There are 6 outcomes where we roll a pair (1,1) ... (6,6)

So probability in (a) is 6 / 36 = 1 / 6

In (b) outcomes where we get sum less than 7

(1,1) (1,2) (1,3) (1,4) (1,5)

(2,1) (2,2) (2,3) (2,4)

(3.1) (3,2) (3,3)

(4,1) (4,2)

(5,1)

So 15 outcomes.

So 21 outcomes where a sum less than 7 is not rolled

So probability is 21/36 = 7/12