# Two dice are thrown. Find the probability that the sum is 8 or greater than 8, if 3 appears on the first die

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Two dice are thrown. Find the probability that the sum is 8 or greater than 8, if 3 appears on the first die.

(a)$\frac{3}{8}$

(b) $\frac{1}{2}$

(c) $\frac{1}{3}$

(d) $\frac{7}{8}$

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Answer: (C)  $\frac{1}{3}$

Let A: Event of getting a sum of 8 or greater than 8 in a throw of two dice

B: Event of getting 3 on the first dice.

Then, A = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2), (3, 6), (4, 5), (5, 4), (6, 3), (4, 6), (6, 4), (5, 5), (5, 6), (6, 5), (6, 6)}.

⇒ n(A) = 13

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

⇒ n(B) = 6

A ∩ B = {(3, 5), (3, 6)} ⇒ n(A ∩ B) = 2.

∴ P(Event of getting sum = 8 or > 8 when 3 appears on the first dice)

⇒ The occurrence of event A on the satisfaction of condition B