JEE PYQ: Probability Question 1
Question 1 - 2021 (16 Mar Shift 1)
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is:
(1) $\frac{3}{4}$
(2) $\frac{52}{867}$
(3) $\frac{39}{50}$
(4) $\frac{22}{425}$
Show Answer
Answer: (3)
Solution
Let $E_1$: missing card is spade, $P(E_1) = \frac{1}{4}$, $P(\overline{E_1}) = \frac{3}{4}$. $A$: two drawn cards are spades. Using Bayes’ theorem: $P(\overline{E_1}|A) = \frac{P(\overline{E_1}) \cdot P(A|\overline{E_1})}{P(A)} = \frac{\frac{3}{4} \times \frac{{}^{13}C_2}{{}^{51}C_2}}{\frac{1}{4} \times \frac{{}^{12}C_2}{{}^{51}C_2} + \frac{3}{4} \times \frac{{}^{13}C_2}{{}^{51}C_2}} = \frac{39}{50}$.
BETA
