Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityMedium
A card is drawn from a standard deck of 52 cards, then replaced, and a second card is drawn. What is the probability that both cards drawn are aces?
- A1/2652
- B1/221
- C1/13
- D1/169
Show answer & explanationAnswer & explanation
Correct answer: D. 1/169
There are 4 aces in a standard 52-card deck. 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. For independent events, P(A and B) = P(A) * P(B). So, (1/13) * (1/13) = 1/169.
Why the other options are wrong
- A. Incorrect calculation.
- B. This would be the probability if the first ace was NOT replaced (4/52 * 3/51).
- C. This is the probability of drawing a single ace, not two aces.
Independent Events Probability
Two events are independent if the outcome of one does not affect the outcome of the other.
- P(A and B) = P(A) * P(B).
- Common in 'with replacement' scenarios or events with no causal link.
- The probability of the second event is the same regardless of the first.
Memory trick: No link, just multiply.