Question -
Answer -
We know that therepeated tosses of a pair of dice are known as Bernoulli trials.
Let the number oftimes of getting doublets in an experiment of throwing two dice simultaneouslyfour times be x.
Thus, q = 1 – p = 1 –1/6 = 5/6
Now, here x has abinomial distribution, where n = 4, p = 1/6, q = 5/6
Thus, P(X = x) = nCx qn-x px,where x = 0, 1, 2, … n
= 4Cx (5/6)4-x (1/6)x
= 4Cx (54-x/66)
Hence, Probability ofgetting 2 successes = P(X = 2)
= 4C2 (54-2/64)
= 6 (52/64)
= 6 × (25/1296)
= 25/216