Find the probability of getting 5 exactly twice in 7 throws of a die.

In this question, let us assume X represent the number of times of getting 5 in 7 throws of the die

Also, the repeated tossing of a die are the Bernoulli trials

Thus, probability of getting 5 in a single throw,

And,

Clearly, we have X has the binomial distribution where n = 7 and

∴

Hence, probability of getting 5 exactly twice in a die = P (X = 2)

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