Find the indicated probability. Round your answer to 6 decimal places when necessary
If you are dealt two cards successfully (with replacement of the first) from a standard 52- card deck, find the probability of getting a heart on the first card and a diamond on the second.
In fraction form
There are a total of 52 cards in a standard deck, and since we are replacing the first card after it is drawn, the total number of cards remains the same.
The probability of getting a heart on the first card is 13/52 because there are 13 hearts in a deck of 52 cards.
Once the first card is replaced, there are still 52 cards in the deck, but now there are only 12 diamonds remaining, so the probability of getting a diamond on the second card is 12/52.
To find the probability of both events occurring, we multiply the probabilities:
P(heart on first card and diamond on second card) = (13/52) * (12/52) = 1/17
Therefore, the probability of getting a heart on the first card and a diamond on the second card is 1/17 in fraction form.