Let two cards be dealt successively, without replacement, from a standard 52-card deck. Find the probability of the event.
The first card is a seven and the second is a seven.
The probability that the first card is a seven and the second is a seven is (Simplify your answer. Type an integer or a fraction.)
Answer
Final Answer: The probability that the first card is a seven and the second is a seven is \(\boxed{\frac{1}{221}}\).
Step 1 ：There are 4 sevens in a deck of 52 cards. So the probability that the first card drawn is a seven is \(\frac{4}{52}\) or \(\frac{1}{13}\).
Step 2 ：After one seven is drawn, there are now 3 sevens left in a deck of 51 cards. So the probability that the second card drawn is a seven is \(\frac{3}{51}\) or \(\frac{1}{17}\).
Step 3 ：Since these are independent events, the probability of both events occurring is the product of their individual probabilities.
Step 4 ：Final Answer: The probability that the first card is a seven and the second is a seven is \(\boxed{\frac{1}{221}}\).
