While shuffling a pack of 52 cards, one card was accidently dropped. Find the probability that the dropped card
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
Total cards = 52. Face cards (kings, queens, jacks) = 12.
(i) P(not a face card)
Number of non-face cards = 52 – 12 = 40
$$P(\text{not a face card}) = \frac{40}{52} = \frac{10}{13}$$
(ii) P(a black king)
There are 2 black kings (king of spades and king of clubs).
$$P(\text{black king}) = \frac{2}{52} = \frac{1}{26}$$
Source: Chapter 14 – Probability, Section 14.1
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Explanation
- A standard deck has 52 cards: 4 suits (spades, clubs — black; hearts, diamonds — red), 13 cards each.
- Face cards = kings + queens + jacks = 4 + 4 + 4 = 12.
- Black kings = king of spades + king of clubs = 2.
- Examiners expect the formula, substitution, and simplified fraction for each part. Always simplify the fraction fully.