Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityMedium
A card game uses a standard deck of 52 cards. A player draws a card, notes its value, and replaces it. Then, the player draws a second card. What is the probability that both cards drawn are aces?
- A1/169
- B1/221
- C1/2704
- D1/676
Show answer & explanationAnswer & explanation
Correct answer: A. 1/169
Since the card is replaced, the two draws are independent events. There are 4 aces in a standard deck of 52 cards. The probability of drawing an ace on the first draw is 4/52 = 1/13. Since the card is replaced, the probability of drawing an ace on the second draw is also 4/52 = 1/13. To find the probability of both events occurring, multiply the individual probabilities: (1/13) * (1/13) = 1/169.
Why the other options are wrong
- B. This would be the probability if the events were dependent (without replacement) for the second card.
- C. This would be the probability of drawing two specific aces (e.g., Ace of Spades then Ace of Clubs) if there were only 4 aces and 52 cards, and the first was replaced.
- D. This is a common distractor, possibly from errors like (4/52)*(3/51) if not replaced but incorrect math.
Independent Probability
The probability of two or more independent events occurring, where the outcome of one event does not affect the outcome of the others.
- Events are 'with replacement' or naturally separate.
- Sample space remains constant for each event.
- Calculated by multiplying individual probabilities.
Memory trick: Independent: Each event stands alone, multiply their chances.