Box I contain 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

$\begin{array}{l}\text{ Given that Box- I contains the numbers }1,2,3,\dots ,30\text{ . Among all these numbers there are }10\\ \text{ prime numbers }2,3,5,7,11,13,17,19,23,29\text{ . }\end{array}$

$\begin{array}{l}\text{ The Box -II contains the numbers }31,32,33,\dots ,50\text{ . Among all these numbers there are }5\text{ prime }\\ \text{ numbers }31,37,41,43,47\end{array}$

$\text{ The required probability is }\frac{\frac{1}{2}\times \frac{20}{30}}{\frac{1}{2}\times \frac{20}{30}+\frac{1}{2}\times \frac{15}{20}}=\frac{\frac{2}{3}}{\frac{2}{3}+\frac{3}{4}}=\frac{2}{3}\times \frac{12}{17}=\frac{8}{17}$