Question

A weighted coin with the probability of showing a head is $\frac{2}{3}$ is tossed. If head appears, then a number is selected from the first $20$ natural numbers otherwise a number is selected from the first $9$ natural numbers. The probability of getting an even number is

• A. $\frac{1}{2}$
• B. $\frac{13}{27}$
• C. $\frac{10}{27}$
• D. $\frac{5}{13}$

Answer 1

Answer: (B)

$P\left(H\right)=\frac{2}{3},P\left(T\right)=\frac{1}{3}$
$A=$ the selected number is an even number
$P\left(A\right)=P\left(H\right)P\left(\frac{A}{H}\right)+P\left(T\right)\cdot P\left(\frac{A}{T}\right)$
$=\frac{2}{3}\times \frac{10}{20}+\frac{1}{3}\times \frac{4}{9}=\frac{1}{3}+\frac{4}{27}=\frac{13}{27}$