Question

Two dice are thrown, find the probability of each of the following events:
P is the event that the sum of the scores on the uppermost faces is a multiple of 6.
Q is the event that the sum of the scores on the uppermost faces is at least 10.
R is the event that same score on both dice.

Answer 1

Given:
Two dice are thrown.
Sample space (S) = {(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)}

$\Rightarrow$ n(S) = 36
Now,
P is the event that the sum of the scores on the uppermost faces of the dice is a multiple of 6.
Thus, we have:
P = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 6)}
∴ n(P) = 6

Hence, P(P) $=\frac{6}{36}=\frac{1}{6}$

Q is the event that the sum of the scores on the uppermost faces of the dice is at least 10.

Thus, we have:

Q = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}

∴ n(Q) = 6

Hence, P(Q) $=\frac{6}{36}=\frac{1}{6}$

R is the event that same score is obtained on both dice.

Thus, we have:

R = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}

∴ n(R) = 6

Hence, P(R) $=\frac{6}{36}=\frac{1}{6}$