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,
