Two dice are thrown : 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.

(iii) Two dice are thrown :
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.

Sol. When two dice are thrown
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) }
∴  n (S) = 36
P is the event that sum of scores on the uppermost faces is a multiple of 6
P = { (1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 6) }
∴  n (P) = 6
Q is the event that sum of scores on the uppermost faces is atleast 10.
Q = { (4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6) }
∴  n (Q) = 6
R is the event that same score on both the dice
R = { (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) }

∴  n (R) = 6

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