Question

There are four boxes $A_1,A_2,A_3$ and $A_4$. Box $A_i$ has i cards and on each card a number is printed, the numbers are from 1 to i. A box is selected randomly, the probability of selection of box $A_i$ is $\frac{i}{\sum i}$ and then a card is drawn. Let $E_i$ represents the event that a card with number 'i' is drawn.

$P\left(E_1\right)$ is equal to

• A. $\frac{1}{5}$
• B. $\frac{1}{10}$
• C. $\frac{2}{5}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C

$\frac{2}{5}$

$P\left(E_1\right)=\frac{1}{10}\times 1+\frac{2}{10}\times \frac{1}{2}+\frac{3}{10}\times \frac{1}{3}+\frac{4}{10}\times \frac{1}{4}=\frac{2}{5}$