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.

Given: head is 3 times as likely to occur as tail.

Now, let the probability of getting a tail in the biased coin be x.


P(T) = x


And P(H) = 3x


For a biased coin, P(T) + P(H) = 1


x + 3x = 1


4x = 1


x = 1/4


Hence, P(T) = 1/4 and P(H) = 3/4


As the coin is tossed twice, so the sample space is {HH, HT, TH, TT}


Let X be a random variable representing the number of tails.


Clearly, X can take the value of 0, 1 or 2.


P(X = 0) = P(no tail) = P(H) × P(H)


P(X = 1) = P(one tail) = P(HT) × P(TH)


P(X = 2) = P(two tail) = P(T) × P(T)


Hence, the required probability distribution is,


X



0



1



2



P(X)









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