Question

A biased coin has a property that probability of occurence of head is twice that of tail. What is the probability that if the coin is tossed twice then the head occurs atleast once?

• A. 2×(2/3)²
• B. 1/6
• C. 1/3
• D. (2/3)²

Answer 1

The correct option is A

2×(2/3)²

$P\left(H\right)=2\times P\left(T\right)$

$P\left(H\right)+P\left(T\right)=1$

$P\left(H\right)=\frac{2}{3}$

$P\left(T\right)=\frac{1}{3}$

$P$(Head occurs atlest once)$=1-P$(No head occurence) $=1-\frac{1}{9}=\frac{8}{9}=2\times (\frac{2}{3}{)}^2$