Question

A standard 52-card deck of French playing cards consists of four suits: hearts, spades, clubs, and diamonds. There are 13 cards of each suit; each suit has cards of rank 2 through 10, along with an ace, king, queen, and jack. Typically, hearts and diamonds are the red suits, while spades and clubs are the black suits. Four cards are drawn from the deck, one at a time, without replacement. a) The second card drawn is from a red suit. Based on this information, what is the probability it is a heart

Answer 1

P = 0.5

Explanation:

Let's call A the event that the second card is red suit and B the event that the second card is a heart.

So, the probability that the second card is a heart given that is a red suit is calculated as:

P(B/A) = P(A∩B)/P(A)

Additionally, the probability P(A∩B) that the second card is a red suit and is a heart is equal to the probability P(B) that the second card is a heart. So,

P(B/A) = P(B)/P(A)

Then, P(A) is equal to 0.5 because half of the cards are red cards and P(B) is equal to 0.25 because a quarter of the cards are red. Finally, P(B/A) is equal to:

P(B/A) = 0.25/0.5 = 0.5