Probability
Conditional probability with lost card
nta_pyq_2025_apr
Grade 12
Question:
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 11 50 , the n is equal to
Step-by-Step Solution
Key Concept: Compute the favourable cases for conditional probability with lost card and divide by the total equally likely cases.
n cards are drawn \& are found all spade, thus remaining$spades = 13 - x$remaining total$cards = 52 - x$(2) Now given that P( lost card is spade$)= 11$50$13-n$$C_{1}$11$i.e. = 52-n$$C_{1}$50$50(13 - n) = 11(52 - n)$$39n = 78$$n = 2$
Correct Answer: 2