4. Probability
Multiplication Rule: Dependent Events
Struggling with Statistics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
What is the probability that a card player draws two aces from a standard deck of 52 cards if they keep the first card after drawing it?
A
0.0035
B
0.0059
C
0.0045
D
0.0044
Verified step by step guidance1
Step 1: Understand the problem. A standard deck of cards has 52 cards, and there are 4 aces in the deck. The player draws two cards sequentially, keeping the first card after drawing it. This means the total number of cards remains 52 for both draws.
Step 2: Calculate the probability of drawing an ace on the first draw. Since there are 4 aces in the deck, the probability is given by \( P(\text{First Ace}) = \frac{4}{52} \).
Step 3: Calculate the probability of drawing an ace on the second draw. Since the first card is kept, the total number of cards remains 52, and there are still 4 aces in the deck. Thus, the probability is \( P(\text{Second Ace}) = \frac{4}{52} \).
Step 4: Multiply the probabilities of the two independent events (drawing an ace on the first draw and drawing an ace on the second draw). The combined probability is \( P(\text{Two Aces}) = P(\text{First Ace}) \times P(\text{Second Ace}) = \frac{4}{52} \times \frac{4}{52} \).
Step 5: Simplify the expression \( \frac{4}{52} \times \frac{4}{52} \) to find the final probability. This will give you the probability of drawing two aces under the given conditions.
3:47mWatch next
Master Multiplication Rule: Dependent Events with a bite sized video explanation from Patrick
Start learning
