Question

in a standard deck of playing cards, each suit has 13 cards, where 2 suits are red (hearts and diamonds) and 2 suits are black (spades and clubs).

what is the conditional probability of drawing a heart, given that the card is red?

use the keypad to enter the answer in the box.

the probability of drawing a heart, given that the card is red, is .

Explanation:

Identify the given information and target event

The total number of red cards in a standard deck is:

$$ n(\text{Red}) = 13 \text{ (hearts)} + 13 \text{ (diamonds)} = 26 $$

The number of cards that are both hearts and red is:

$$ n(\text{Heart} \cap \text{Red}) = 13 $$

Apply the conditional probability formula

The conditional probability of drawing a heart given that the card is red is:

$$ P(\text{Heart} \mid \text{Red}) = \frac{n(\text{Heart} \cap \text{Red})}{n(\text{Red})} = \frac{13}{26} $$

Simplify the fraction

$$ P(\text{Heart} \mid \text{Red}) = \frac{1}{2} = 0.5 $$

Answer:

The probability of drawing a heart, given that the card is red, is <blank>\(\frac{1}{2}\)</blank>.