In a deck of 52 cards, what is the probability of drawing a heart given that the

₹0.0

Question: In a deck of 52 cards, what is the probability of drawing a heart given that the card drawn is a red card?

Options:

Correct Answer: 1/2

Solution:

There are 26 red cards (hearts and diamonds). The number of hearts is 13. Thus, P(Heart | Red) = 13/26 = 1/2.

In a deck of 52 cards, what is the probability of drawing a heart given that the card drawn is a red card?

In a deck of 52 cards, what is the probability of drawing a heart given that the card drawn is a red card?

Step 1: Understand that a standard deck has 52 cards.
Step 2: Identify the red cards in the deck. There are two suits that are red: hearts and diamonds.
Step 3: Count the total number of red cards. There are 13 hearts and 13 diamonds, so 13 + 13 = 26 red cards.
Step 4: Determine how many of the red cards are hearts. There are 13 hearts.
Step 5: Calculate the probability of drawing a heart given that the card drawn is a red card. This is done by dividing the number of hearts by the total number of red cards: 13 hearts / 26 red cards.
Step 6: Simplify the fraction 13/26 to get 1/2.

Conditional Probability – The probability of an event occurring given that another event has already occurred.
Sample Space – Understanding the total number of outcomes in a given scenario, in this case, the total number of red cards.
Event Counting – Counting the number of favorable outcomes (hearts) versus the total outcomes (red cards).