# 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. - Mathematics and Statistics

Sum

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.

#### Solution

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)
Concept: Random Variables and Its Probability Distributions
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 8 Probability Distributions
Exercise 8.1 | Q 1.07 | Page 141