Q1. [2] § Chapter Opening and Epigraph
In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is queen of heart, if the lost card is a black card.
Previously asked in CBSE board exam
2024 30/1/1 Q22
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
Since the lost card is a black card, the remaining cards = 52 – 1 = 51.
There is only 1 queen of heart in the deck, and since the lost card is black (not the queen of heart), the queen of heart is still present among the remaining cards.
$$P(\text{queen of heart}) = \frac{1}{51}$$
Source: Chapter 14 – Probability, Section 14.1
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Explanation
- Key point: the lost card is a black card (clubs or spades). The queen of heart is a red card, so it is definitely still in the remaining 51 cards → favourable outcomes = 1.
- Total outcomes = 51 (not 52), because one card is already lost.
- Many students mistakenly write 52 in the denominator — always reduce by the number of lost/removed cards.
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