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# A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes. - Mathematics and Statistics

Sum

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

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#### Solution

Let X = number of doublets.

p = probability of getting a doublet when a pair of dice is thrown

∴ p = 6/36 = 1/6 and

q = 1 - p = 1 - 1/6 = 5/6

Given: n = 4

∴ X ~ B(4, 1/6)

The p.m.f. of X is given by

P(X = x) = "^nC_x  p^x  q^(n - x)

i.e. p(x) = "^nC_x (1/6)^x (5/6)^(4 - x), x = 0, 1, 2, 3, 4

∴ P(2 successes) = P(X = 2)

= p(2) = "^4C_2 (1/6)^2 (5/6)^(4 - 2)

= (4!)/(2!*2!) (1/6)^2 (5/6)^2

= (4 * 3 * 2!)/(2!.2.1) xx 1/36 xx 25/36

= 25/216

Hence, the probability of two successes is 25/216.

Concept: Binomial Distribution
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