Question

(i) 3 Coin are tossed and X be the number of heads turning up. Write probability distribution of X.

(ii) There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

Answer 1

(1) S = { HHH , HHT ,HTH, THH, HTT , THT , HTH , TTT)

Let X denotes the random variable of getting a Head. Then X can take values 0,1 ,2,3.

P(X = 0) = P(no Heads)

= P({TTT})

P(X = 3 ) = P(3 Heads)

= \(P(H)\times P(H)\times P(H)\\=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\\=\frac{1}{8}\)

(ii) Let X denotes the random variable of number of defective items. Clearly X has a Binomial Distribution with n = 10