Question

a pair of dice is rolled. find the probability of rolling a sum not less than 3

Answer 1

A pair of dice is rolled. Two dice are rolled

Possible outcomes 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)

So total of 36 outcomes

Question says 'the probability of rolling a sum not less than 3'

we look at the pair that has sum greater than or equal to 3

There is only one pair (1,1) whose sum is 1+1 =2

So we ignore (1,1) pair

Remaining 35 pairs have sum greater than 3

the probability of rolling  = (number of times event occurs)  divide by total number of outcomes

the probability ( rolling a sum not less than 3) = $\frac{35}{36}$