Question

There are four boxes $B_1,B_2,B_3$ and $B_4$. Box $B_1$ 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 selecting box $B_i$ is $\frac{i}{10}$ and a card is drawn. Let $E_i$ represent the event that a card with number ' $i$ ' is drawn.
$P\left(E_1\right)$ is equal to

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

Answer 1

Answer: (D)

$P\left(B_1\right)=\frac{1}{10};P\left(B_2\right)=\frac{2}{10};P\left(B_3\right)=\frac{3}{10};P\left(B_4\right)=\frac{4}{10}$
$P\left(E_1\right)=\frac{1}{10}\times (1)+\left(\frac{2}{10}\times \frac{1}{2}\right)+\left(\frac{3}{10}\times \frac{1}{3}\right)+\left(\frac{4}{10}\times \frac{1}{4}\right)=\frac{4}{10}=\frac{2}{5}$