Question

A coin is biased so that the head is $3$ times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

Answer 1

Given a biased coin such that heads is 3 times as likely as tails. The coin is tossed twice.

P(H) = 3434 and P(T) = 1414

Let X be the random variable for the number of tails.

P (X = 0) = P (HH) =3/4*3/4=9/1634×34=916

P (X = 1) = P (HT, TH) =3/4*1/4+3/4*1/4=3/834×14+34×14=38

P (X = 2) = P (TT) = 1/4*1/4=1/16
14×14=116

Therefore the probability distribution is as follows:

X : P(X)

0 9/16

1 3/8

2 1/16