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 $\frac{11}{50}, \text{ then } n \text{ is equal to}$ _______

Question

A bag contains 10 balls out of which $ k $ are red and $ (10-k) $ are black, where $ 0 \le k \le 10 $. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is:

Answer 1

Given that $ n $ cards are drawn and observed to be spades, the number of spades remaining is $ 13 - x $, where $ x $ represents the number of spades drawn. Consequently, the total number of cards remaining is $ 52 - x $.
The probability that the lost card is a spade is provided as $ \frac{11}{50} $. This probability can be expressed as:

\[P(\text{lost card is spade}) = \frac{\binom{13 - x}{1}}{\binom{52 - x}{1}} = \frac{11}{50}\]

Solving this equation for $ x $ yields $ x = 2 $. Therefore, the number of cards drawn, $ n $, is $ 2 $.

The correct answer is $ 2 $.

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 $\frac{11}{50}, \text{ then } n \text{ is equal to}$ _______

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Correct Answer: 2

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