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

Solution:

Bernoulli trials are defined as the repeated tosses of a pair of dice. Let x be the number of times you get doublets in an experiment where you throw two dice at the same time four times.

Probability of getting a pair of doublets in a single roll of the dice (p)

Thus, q=1-p=1-1 / 6=5 / 6

Now, here x has a binomial distribution, where n=4, p=1 / 6, q=5 / 6

Thus, \mathrm{P}(\mathrm{X}=\mathrm{x})={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{x}} \mathrm{q}^{\mathrm{n}-\mathrm{x}} \mathrm{p}^{\mathrm{x}}, where \mathrm{x}=0,1,2, \ldots \mathrm{n}

={ }^{4} C_{x}(5 / 6)^{4-x}(1 / 6)^{x}

=6\left(5^{2} / 6^{4}\right)

=6 \times(25 / 1296)

= 25/216

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