Question

You draw a card at random from a standard deck of 52 cards. Find the following conditional probabilities: a.) The probability that a card is a heart, given that it is red?

Answer 1

To find the probability that a card is a heart, given that it is red, we can use conditional probability. The probability that a card is a heart, given that it is red, is 0.5.

Step-by-step explanation:

To find the probability that a card is a heart, given that it is red, we can use conditional probability. Let's denote the event that a card is a heart as H and the event that a card is red as R. We want to find P(H|R), the probability that a card is a heart given that it is red.

Since there are 26 red cards in a standard deck of 52 cards and 13 of these red cards are hearts, we can calculate P(H|R) as:

P(H|R) = P(H ∩ R) / P(R)

P(H ∩ R) represents the probability that a card is both a heart and red, which is 13/52 = 1/4. And P(R) represents the probability that a card is red, which is 26/52 = 1/2.

Therefore, the conditional probability P(H|R) is:

P(H|R) = (1/4) / (1/2) = 1/2 = 0.5.