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 :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) →
| x | 0 | 1 | 2 |
| P(x) | 9/16 | 6/16 | 1/16 |
$P(Head)=3P(Tail)$
$⇒P(Head)+P(Tail)=1$
$⇒3P(Tail)+P(Tail)=1$
$⇒P(Tail)=\frac{1}{4}$
$P(Tail=0)=\frac{3}{4}×\frac{3}{4}=\frac{9}{16}$
$P(Tail=1)=\frac{3}{4}×\frac{1}{4}×2=\frac{6}{16}$
$P(Tail=2)=\frac{1}{4}×\frac{1}{4}=\frac{1}{16}$