Question

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

Answer 1

P(Head) = `3/4`, P(Tail) = `1/4`

Let X be the number of tails in two tosses:

X	0	1	2
	`3/4 xx 3/4`	`2 xx 3/4 xx 1/4`	`1/4 xx 1/4`
P(X)	`9/16`	`6/16`	`1/16`

Mean = ΣXP(X)

= `0 xx 9/16 + 1 xx 6/16 + 2 xx 1/16`

= `0 + 6/16 + 2/16`

= `8/16`

= `1/2`