A card is drawn from a standard deck of 52 cards. What is the probability that t
Practice Questions
Q1
A card is drawn from a standard deck of 52 cards. What is the probability that the card is a heart given that it is a red card?
1/2
1/4
1/3
2/3
Questions & Step-by-Step Solutions
A card is drawn from a standard deck of 52 cards. What is the probability that the card 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 only interested in the red cards since the question specifies that the card drawn is red.
Step 3: Count the number of hearts among the red cards. There are 13 hearts.
Step 4: Count the total number of red cards. There are 26 red cards (hearts + diamonds).
Step 5: Calculate the probability of drawing a heart given that the card is red. 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 relevant to the problem.
Event Classification – Identifying and classifying events (e.g., red cards, hearts) within the sample space.
