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

Explanation

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=frac{6}{36}=frac{1}{6} `

`therefore q=1-p=1-frac{1}{6}=frac{5}{6}`

Clearly, `X` has the binomial distribution with `n=4, p=frac{1}{6}, and q=frac{5}{6}`
` therefore {P}({X}=x)=^{n} {C}_{x} q^{n-x} p^{x}, `where `x=0,1,2,3 ldots n`

`=^{4} {C}_{x}(frac{5}{6})^{4-x} cdot(frac{1}{6})^{x}`

`=^{4} {C}_{x} cdot frac{5^{4-x}}{6^{4}}`

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