A card is drawn from a standard deck of 52 cards. What is the probability that i

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Question: A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart given that it is a red card?

Options:

Correct Answer: 1/2

Solution:

There are 26 red cards (hearts and diamonds). The probability of drawing a heart given that it is red is 13/26 = 1/2.

A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart given that it is a red card?

A card is drawn from a standard deck of 52 cards. What is the probability that it is a heart given that it is a red card?

Correct Answer: 1/2

Step 1: Understand that a standard deck has 52 cards, which includes 26 red cards (13 hearts and 13 diamonds).
Step 2: Identify that we are looking for the probability of drawing a heart, but we know the card is red.
Step 3: Since we are only considering red cards, we focus on the 26 red cards.
Step 4: Out of these 26 red cards, 13 are hearts.
Step 5: To find the probability of drawing a heart given that the card is red, we use the formula: Probability = (Number of favorable outcomes) / (Total outcomes).
Step 6: Here, the number of favorable outcomes (hearts) is 13, and the total outcomes (red cards) is 26.
Step 7: Calculate the probability: 13 (hearts) divided by 26 (red cards) equals 1/2.

Conditional Probability – The probability of an event occurring given that another event has already occurred.
Sample Space Reduction – Understanding how the sample space changes when additional information is provided.