Question

For these questions, assume that we have a standard 52 card deck. Compute the probabilities below, explaining your reasoning by counting outcomes and/or using probability formulas. Give your answer as fractions in lowest terms.

a. Suppose you draw a card at random. What is the probability that the card is not a king?
b. Suppose you draw two card at random without replacement. What is the probability that the second card is a diamond given that the first was a diamond?

Answer 1

The probability of drawing a card that is not a king is 12/13. The probability of the second card being a diamond, given that the first card was a diamond, is 12/51.

Step-by-step explanation:

a. To calculate the probability of drawing a card that is not a king, we need to determine the number of cards that are not kings and divide it by the total number of cards in the deck. There are 4 kings in the deck, so the number of cards that are not kings is 52 - 4 = 48. Therefore, the probability of drawing a card that is not a king is 48/52, which simplifies to 12/13.

b. To calculate the probability of the second card being a diamond, given that the first card was a diamond, we need to determine the number of diamonds remaining in the deck after the first card is drawn and divide it by the total number of remaining cards. There are 13 diamonds in the deck, so after one diamond is drawn, there are 13 - 1 = 12 diamonds remaining. The total number of remaining cards is 52 - 1 = 51. Therefore, the probability of the second card being a diamond, given that the first card was a diamond, is 12/51, which does not simplify further.