A coin is biased so that the head is 3 times likely to occur as tail. If the coin is tossed twice, then the probability distribution of number of tails is :

The correct answer is Option (1) → 

$P(Head)=3P(Tail)$

$⇒P(Head)+P(Tail)=1$

$⇒3P(Tail)+P(Tail)=1$

$⇒P(Tail)=\frac{1}{4}$

$P(Tail=0)=\frac{3}{4}×\frac{3}{4}=\frac{9}{16}$

$P(Tail=1)=\frac{3}{4}×\frac{1}{4}×2=\frac{6}{16}$

$P(Tail=2)=\frac{1}{4}×\frac{1}{4}=\frac{1}{16}$