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Question
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes
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Solution
In a throw of a pair dice the doublets are (1, 1),(1, 2) (3, 3),(4, 4),(5, 5),(6, 6)
Probability of getting a doublet P = `6/36 = 1/6`
⇒ q = 1 – q = `56` and n = 4 is given
The probability of success = `[(4),(x)] [(1),(6)]^x [(5),(6)]^(4 - x)`
Therefore the probability of 2 success are
P(X = 2) = `(4/2)(1/6)^2(5/6)^(4 - 2)`
= `(4 xx 3)/(1 xx 2) xx 1/36 xx 25/36`
= `6 xx 1/36 xx 25/36`
= `1/6 xx 25/36`
= `25/216`
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