Question

You are randomly choosing cards , one at a time and with replacement, from a standard deck of cards. Find the probability that you choose an ace, then a red card, and then a face. (Remember that face cards are jacks, queens, and kings)

Answer 1

B) two number cards, two face cards, one number card and one face card

Explanation:

Since order doesn't matter all you need to know is whether you got two number cards, two face cards, or one number card and one face card.

Answer 2

Since the cards are being replaced, the total number of cards in the deck remain the same and the probability of picking one card is not affecting the probability of next cards.

Total number of cards in the deck = 52
Number of Aces = 4
Number of Red Cards = 26
Number of Face Cards = 12

Probability of picking an Ace = 4/52
Probability of picking a Red Card = 26/52
Probability of picking a Face Card = 12/52

The probability of picking an ace, then a red card, and then a face card will be =
`(4)/(52)* (26)/(52)* (12)/(52) = (3)/(338)`

Thus the probability of picking an ace, then a red card, and then a face card will be 3/338