Consider a deck of 52 playing cards. We draw 2 cards without replacement and let A be the event that the first card is ace and B be the event that both cards are an ace. Find B given A.
Why is the probablility of B given A not 3/51? This should be the probability of the second card you draw being an ace given the first one is an ace. I thought these probabilities would be equal but they are not the answer is 1/51.
Thanks for your help
Best Answer
It should be $\frac{3}{51}$.
$$P(B|A) = \frac{P(A\cap B)}{P(A)}= \frac{\frac{4}{52}\cdot \frac{3}{51}}{\frac{4}{52}}$$