Let two cards be dealt successively, without replacement, from a standard 52-card deck. Find the probability of the event.
spade dealt second, given a spade dealt first
The probability that the second is a spade, given that the first is a spade is (Simplify your answer. Type an integer or a fraction.)
Answer
Final Answer: The probability that the second card dealt is a spade, given that the first card dealt is a spade is \(\boxed{\frac{12}{51}}\).
Step 1 ：Let two cards be dealt successively, without replacement, from a standard 52-card deck. We are asked to find the probability of the event that a spade is dealt second, given a spade was dealt first.
Step 2 ：The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, we are given that the first card dealt is a spade. This means that there are now 51 cards left in the deck, 12 of which are spades.
Step 3 ：So, the probability that the second card dealt is a spade is \(\frac{12}{51}\).
Step 4 ：Final Answer: The probability that the second card dealt is a spade, given that the first card dealt is a spade is \(\boxed{\frac{12}{51}}\).
