Question

What is the probability of drawing at random the 4♥ and the 9♣ from a deck of cards on two successive draws?

Answer 1

Find each probability and multiply them.

Answer 2

Depends on whether the first card is returned to the deck before the second is drawn, and whether the order counts. If it is replaced and the order counts, the probability is\[P (4H, 9C)=(\frac{1}{52})^2\]If the first card is not replaced and the order counts, it looks like\[P (4H, 9C)=\frac{1}{52}\frac{1}{51}\]If the first card is replaced and the order doesn't matter,\[P (4H, 9C)=\frac{2}{52}\frac{1}{52}\]Finally, if the card is not replaced, and order doesn't matter, \[P (4H, 9C)=\frac{2}{52}\frac{1}{51}\]

Answer 3

As mentioned by mathstudent55 above, these are the products of the single-event probabilities.