Fewpal
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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

= P(A/B) = \(\frac{P(A\,\cap\,B)}{P(A)}\) = \(\frac{\frac{n(A\,\cap\,B)}{n(S)}}{\frac{n(B)}{n(S)}}\) = \(\frac{n(A\,\cap\,B)}{n(B)}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)

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