Question

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to $50 .$ A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is :

• A. $\frac{8}{17}$
• B. $\frac{2}{3}$
• C. $\frac{4}{17}$
• D. $\frac{2}{5}$

Answer 1

Answer: (A)

Let $B _{1}$ be the event where $Box - I$ is selected. $\& B _{2} \rightarrow$ where box-II selected
$P \left( B _{1}\right)= P \left( B _{2}\right)=\frac{1}{2}$
Let $E$ be the event where selected card is non prime.
For $B _{1}:$ Prime numbers
$\{2,3,5,7,11,13,17,19,23,29\}$
For $B _{2}:$ Prime numbers :
$\{31,37,41,43,47\}$
$ P ( E ) = P \left( B _{1}\right) \times P \left(\frac{ E }{ B _{1}}\right)+ P \left( B _{2}\right) P \left(\frac{ E }{ B _{2}}\right)$
$=\frac{1}{2} \times \frac{20}{30}+\frac{1}{2} \times \frac{15}{20} $
Required probability
$P \left(\frac{ B _{1}}{ E }\right)=\frac{\frac{1}{2} \times \frac{20}{30}}{\frac{1}{2} \times \frac{20}{30}+\frac{1}{2} \times \frac{15}{20}}$
$=\frac{\frac{2}{3}}{\frac{2}{3}+\frac{3}{4}}=\frac{8}{17}$