Question

A coin is biased so that the head is 3 times as likely to occur as tail. Find the probability distribution of number of tails in two tosses.

Answer 1

Let X denote the number of tails.
∴ Possible values of X are 0, 1, 2.
Let P(getting tail) = p
According to the given condition,
P(getting head) = q = 3p
As p + q = 1,
p + 3p = 1

∴ p = `(1)/(4)  "and " "q" = (3)/(4)`

∴ P(X = 0) = P(no tails) = qq = q² = `(3/4)^2 = (9)/(16)`

P(X = 1) = P(one tail) = pq + qp = 2pq = `2(1/4)(3/4) = (6)/(16)`

P(X = 2) = P(two tails) = pp = p² = `(1/4)^2 = (1)/(6)`

∴ Probability distribution of X is as follows:

X	0	1	2
P(X = x)	`(9)/(16)`	`(6)/(16)`	`(1)/(16)`