Question

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

Answer 1

The repeated tosses of a pair of dice are Bernoulli trials. Let X denote the number of times of getting doublets in an experiment of throwing two dice simultaneously four times.

Probability of getting doublets in a single throw of the pair of dice is

`p = 6/36`

= `1/6`

∴ q = 1 – p

= `1 - 1/6`

= `5/6`

Clearly, X has the binomial distribution with n = 4, `p = 1/6` and `q = 5/6`

∴ `P(X = x) = ""^nC_x q^(n - x)p^x`, where x = 0, 1, 2, 3 ... n

 = `""^4C_x (5/6)^(4  -  x) * (1/6)^x`

= `""^4C_x * 5^(4  -  x)/6^4`

∴ P(2 successes) = P(X = 2)

= `""^4C_2 * 5^(4  -  2)/6^4`

= `6 * (25)/(1296)`

= `(25)/(216)`