JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Probability

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A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is

\frac{11}{50}

, the n is equal to

Answer: 2

Solution

By Bayes' theorem, drawing

n

spades from the remaining

51

cards makes the lost card a spade with probability

\frac{( n 12 )}{( n 12 ) + 3 ( n 13 )} = \frac{13 - n}{52 - n}

. Setting

\frac{13 - n}{52 - n} = \frac{11}{50}

gives

50 (13 - n) = 11 (52 - n)

, so

39 n = 78

and

n = 2

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Integer answer

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