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

Question

Philoid · Accepted Answer

We know that the repeated tosses of a pair of dice are known as Bernouli trials.

Let the number of times of getting doublets in an experiment of throwing two dice simultaneously four times be x.

Thus, P(X = x) = ⁿC_xq^n-xp^x , where x = 0, 1, 2, …n

= ⁴C_x (5/6)^4-x(1/6)^x

= ⁴C_x (5^4-x/6⁶)

Hence, Probability of getting 2 successes = P(X = 2)

= ⁴C₂(5^4-2/6⁴)