Question

Two different dice are thrown together. Find the probability that the numbers obtained have:

1. even sum,
2. even product.

Answer 1

Total Number of possible outcomes = 6² =  6 × 6 = 36  (Two dices are thrown together)

i. Let A be the event of getting an even sum.

Favourable outcome for event A

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

So, there are 18 favourable outcomes.

Therefore, `P(A) = 18/36 = 1/2`.

Hence, the probability of getting an even sum is `1/2`.

ii. Let B be the event of getting an even product.

Favourable outcomes for event B

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

So, there are 27 favourable outcomes.

Therefore, `P(B) = 27/36 = 3/4`.

Hence, the probability of getting an even product is `3/4`.