Multiple choice

Cards are drawn one by one from a deck of 52 cards without replacement. The chance that four cards are drawn before the first ace (fifth card) is

  1. 4 48 × 1 4

  2. 48 × 47 × 46 × 45 × 4 52 × 52 × 52 × 52 × 52 × 4 52

  3. 48 × 47 × 46 × 45 52 × 51 × 50 × 49 × 44 48

  4. 48 × 47 × 46 × 45 52 × 51 × 50 × 49 × 4 48

  5. 1 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To have four cards before the first ace, the first four cards must be non-aces (48/52 * 47/51 * 46/50 * 45/49) and the fifth card must be an ace (4/48).

AI explanation

The probability is found by multiplying the probabilities of drawing four non-aces in succession, followed by an ace. There are 48 non-aces and 4 aces in a 52-card deck. The probability of the first four cards being non-aces and the fifth being an ace is (48 divided by 52) times (47 divided by 51) times (46 divided by 50) times (45 divided by 49) times (4 divided by 48). The result is 48 times 47 times 46 times 45 divided by the product of 52, 51, 50 and 49, times 4 divided by 48.

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