A deck of 52 playing cards has 4 aces. If two cards are drawn without replacement, what is the probability that both cards are aces?
Options
A
1/26
B
1/169
C
1/13
D
1/221
Answer & Analysis
Answer
D
Analysis
Question Analysis
This question involves calculating the probability of drawing two aces from a deck of cards without replacement, which is a classic example of dependent events.
The main focus is on applying the concept of dependent - event probability to a standard deck - of - cards situation.
Key Concept Explanation
In a deck of cards, when one card is drawn, it affects the probabilities for the next draw as the total number of cards and the number of cards of a particular type (in this case, aces) change.
Step-by-Step Solution
Calculate the probability of drawing an ace on the first draw: There are 4 aces in a deck of 52 cards, so .
Calculate the probability of drawing an ace on the second draw given that an ace was drawn on the first draw: After removing one ace, there are 3 aces left in a deck of 51 cards.
So
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