From a pack of 52 cards, two are drawn at random. Find the chance that one is…
2026
From a pack of 52 cards, two are drawn at random. Find the chance that one is a knave and the other a queen.
- A.
1/12
- B.
1/6
- C.
1/9
- D.
8/663
Attempted by 4 students.
Show answer & explanation
Correct answer: D
Classical probability: P(E) = n(E)/n(S), where n(S) is the total number of equally likely ways to select the required items, and n(E) is the number of those ways that satisfy the event. When cards are drawn together (order does not matter), count selections using combinations (nCr), not permutations.
Total ways to draw any 2 cards from the 52-card deck: n(S) = 52C2 = (52×51)/(2×1) = 1326.
A deck has exactly 4 knaves (jacks) and 4 queens. Ways to pick 1 knave from the 4 available: 4C1 = 4.
Ways to pick 1 queen from the 4 available: 4C1 = 4.
Since one knave AND one queen must both be drawn, the favourable count multiplies: n(E) = 4 × 4 = 16.
Probability = n(E)/n(S) = 16/1326.
Simplify by dividing numerator and denominator by their GCD, 2: 16/1326 = 8/663. Since 663 = 3 × 13 × 17 shares no factor with 8, this is fully reduced — confirming the option matching 8/663 is correct.
