A card is drawn from an ordinary deck of cards. What is the probability that the card is an even number given that it is a club? *
Mathematics · High School · Mon Jan 18 2021
Answered on
An ordinary deck of cards contains 52 cards, and each suit (hearts, diamonds, clubs, spades) has 13 cards. Since we are given that the card drawn is a club, there are 13 clubs.
Now, among the clubs, the even-numbered cards are 2, 4, 6, 8, 10, and 12 (10 and 12 being the 10 of clubs and queen of clubs).
So, the probability of drawing an even number given that it is a club is the number of favorable outcomes (even-numbered clubs) divided by the total number of possible outcomes (clubs):
\[ P(\text{even number} | \text{club}) = \frac{\text{Number of even-numbered clubs}}{\text{Total number of clubs}} \]
\[ P(\text{even number} | \text{club}) = \frac{6}{13} \]
Therefore, the probability is \( \frac{6}{13} \).