Question 1171398: A computer randomly deals an ordinary decks of cards for a game of FreeCell, and the first card dealt is a red card. Find the probability that the card was also a heart. Write your answer in exact simplified form.
The probability that the card was also a heart is______
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's break down this probability problem:
* **Total Cards:** An ordinary deck has 52 cards.
* **Red Cards:** There are 26 red cards (13 hearts and 13 diamonds).
* **Hearts:** There are 13 hearts.
We're given that the first card dealt is a red card. We want to find the probability that it was also a heart. This is a conditional probability.
* **P(Heart | Red):** The probability of the card being a heart, given that it's red.
We can use the formula for conditional probability:
* P(Heart | Red) = P(Heart and Red) / P(Red)
* **P(Heart and Red):** Since all hearts are red, P(Heart and Red) is the same as P(Heart).
* P(Heart) = 13/52
* **P(Red):** The probability of drawing a red card.
* P(Red) = 26/52
Now, plug these values into the conditional probability formula:
* P(Heart | Red) = (13/52) / (26/52)
To simplify, multiply the numerator by the reciprocal of the denominator:
* P(Heart | Red) = (13/52) * (52/26)
The 52's cancel out:
* P(Heart | Red) = 13/26
Simplify the fraction:
* P(Heart | Red) = 1/2
Therefore, the probability that the card was also a heart is 1/2.
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