Question

A coin is biased so that a head is 3 times as likely to occur as tail. If the coin is tossed three times 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) = 34×34=91634×34=916

P (X = 1) = P (HT, TH) = 34×14+34×14=3834×14+34×14=38

P (X = 2) = P (TT) = 14×14=11614×14=116

Therefore the probability distribution is as follows: XP(X)09161382116