what is the chance you will draw two hearts in a row if you replace your first card?
Simplified fraction
There are 4 suits, so
P(❤️) = 1/4 for each draw, so ...
To determine the chance of drawing two hearts in a row when replacing your first card, we need to consider the number of hearts in the deck and the total number of cards after the replacement.
Let's assume we have a standard deck of 52 playing cards, which consists of 13 hearts.
After replacing the first card, the total number of cards remains the same while the number of hearts also remains the same at 13. So the probability of drawing a heart in each draw remains constant.
To calculate the probability, we divide the number of favorable outcomes by the number of possible outcomes. In this case, the favorable outcome is drawing two hearts in a row, and the possible outcome is any two cards you draw.
Since we replace the first card, the probability of drawing a heart in the first draw is 13/52 (or 1/4 since 13 divided by 52 equals 1/4).
Since the replacement didn't affect the ratio of hearts to the total cards, the probability of drawing a heart in the second draw is also 13/52 (or 1/4).
When you draw two cards in a row, the probabilities multiplied together. Thus, the probability of drawing two hearts in a row with replacement is:
(13/52) * (13/52) = 169/2704
To simplify this fraction, you can divide both the numerator and denominator by their greatest common divisor, which is 13 in this case:
169/2704 = 13/208
So the probability of drawing two hearts in a row with replacement is 13/208.