from a pack of 52 cards two cards are drawn without replagement.find out the probability that first is of heart and secod is ace?
To find the probability that the first card drawn is a heart and the second card drawn is an ace, we need to calculate the individual probabilities of each event and then multiply them together.
Step 1: Calculate the probability of the first card being a heart.
There are a total of 52 cards in the pack, and 13 of them are hearts. So the probability of drawing a heart as the first card is 13/52.
Step 2: Calculate the probability of the second card being an ace.
After drawing the first card, there are now 51 cards left in the pack. There are 4 aces in the deck, and since we didn't replace the first card drawn, there are only 3 aces left. So the probability of drawing an ace as the second card is 3/51.
Step 3: Multiply the probabilities from Step 1 and Step 2.
The probability of the first card being a heart and the second card being an ace is obtained by multiplying the probabilities:
(13/52) * (3/51) = 39/2652.
Therefore, the probability that the first card drawn is a heart and the second card drawn is an ace is 39/2652, which can be further simplified if needed.