Question

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes

Answer 1

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`