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.

∴ P(H) = `3/4` and P(T) = `1/4`

The coin is tossed twice.

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

Then X can take the value 0, 1, 2.

∴ P(X = 0) = P(HH)

=`3/4 xx 3/4`

= `9/16`

P(X = 1) = P(HT, TH)

=`3/4 xx 1/4 +1/4 xx 3/4`

= `6/16`

= `3/8`

P(X = 2) = P(TT)

= `1/4 xx 1/4`

= `1/16`

Therefore, the required probability distribution is as follows.

X	0	1	2
P(X = x)	`9/16`	`3/8`	`1/16`