Two cards are drawn in succession without replacement from a standard deck of 52 cards. What is the probability that the first card is a heart given that the second card is a clubs?

Question

Quizplus · Accepted Answer

We use Bayes' Theorem to solve this problem. Let A be the event that the first card is a heart and B be the event that the second card is a clubs. Then, we want to find P(A|B). We have:
P(A|B) = P(A and B) / P(B)
We know that P(B) = 13/51 since there are 13 clubs left in the deck out of 51 cards remaining after drawing the first card. To find P(A and B), we can use the multiplication rule:
P(A and B) = P(B|A) * P(A)
P(A) is simply the probability of drawing a heart on the first card, which is 13/52. To find P(B|A), we have 12 clubs left in the deck out of 51 cards remaining after drawing the first heart, so P(B|A) = 12/51. Therefore:
P(A and B) = (12/51) * (13/52) = 3/52
Finally, we can substitute P(A and B) and P(B) back into Bayes' Theorem to get:
P(A|B) = (3/52) / (13/51) = 3/13
So the answer is B, 11eab448_e7eb_b303_acdb_138d72a339b1_TB6027_11.

Two Cards Are Drawn in Succession Without Replacement from a Standard