JEE PYQ: Probability Question 15
Question 15 - 2020 (02 Sep Shift 1)
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:
(1) $\frac{2}{3}$
(2) $\frac{8}{17}$
(3) $\frac{4}{17}$
(4) $\frac{2}{5}$
Show Answer
Answer: (2)
Solution
$P(B_1) = P(B_2) = \frac{1}{2}$. Non-primes in Box I (1-30): 20. Non-primes in Box II (31-50): 15. $P\left(\frac{B_1}{N}\right) = \frac{\frac{1}{2} \times \frac{20}{30}}{\frac{1}{2} \times \frac{20}{30} + \frac{1}{2} \times \frac{15}{20}} = \frac{\frac{1}{3}}{\frac{1}{3} + \frac{3}{8}} = \frac{8}{17}$.
BETA
