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Question
A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of two successes
Solution
Let X denote the number of times of getting doublet.
If a pair of dice is thrown, then there are total 36 possible outcomes, out of which 6 [i.e. (1, 1), (2, 2), …,(6, 6)] are doublets.
∴ P(getting a doublet) = p = `(6)/(36) = (1)/(6)`
∴ q = 1 – p = `1 - (1)/(6) = (5)/(6)`
Given, n = 3
∴ X ∼ B `(3, 1/6)`
The p.m.f. of X is given by
P(X = x) = `""^3"C"_x (1/6)^x (5/6)^(3 - x) ,x ` = 0, 1, 2, 3
∴ P(two successes) = P(X = 2)
= `""^3"C"_2(1/6)^2(5/6)`
= `3 xx (1)/(36) xx (5)/(6)`
= `(5)/(72)`.
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