Question

Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5 and (ii) difference of the numbers on the two dice is 3.

Answer 1

Two dice are thrown.

∴ Total outcomes = 36 which are given by

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1) --- (2, 6), (3, 1) --- (3, 6), (4, 1) --- (4, 6),

(5, 1) --- (5, 6), (6, 1) --- (6, 6)}

P(E) = `"Favorable outcomes"/"Total outcomes"`

(i)  P(sum of the no. 5 on the two dice is 5)

= `({(1, 4), (2, 3), (3, 2), (4, 1)})/36`

= `4/36`

= `1/9`

(ii) P(difference of the no. 5 on the two dice is 3)

= `({(1, 4), (2, 5), (4, 1), (5, 2), (6, 3), (3, 6)})/36`

= `6/36`

= `1/6`