Question

Two coins are tossed. Find the conditional probability that two Heads will occur given that at least one occurs.

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. none of these

Answer 1

Answer: (A)

$\frac{1}{3}$

Let A = {at least one Head occurs}, B = {two Heads occur}

Given:

Two coins are tossed.

To find:

The conditional probability that two Heads will occur given that at least one occurs.

$P\left(B\right)=\frac{P(A\cap B)}{P(A\cup B)}=\frac{P\left(A\right)\times P\left(B\right)}{P\left(A\right)+P\left(B\right)-P\left(A\right)\times P\left(B\right)}=\frac{\frac{1}{2}\times \frac{1}{2}}{\frac{1}{2}+\frac{1}{2}-\frac{1}{2}\times \frac{1}{2}}=\frac{1}{4}\times \frac{4}{2+2-1}=\frac{1}{3}$