Aces
Solve the first problem 18 problems
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- Pair of aces from two decks ●○○○○ 10 ptsA hand consists of one card drawn from a standard 52-card deck with flowers on the back and one card drawn from a standard 52-card deck with birds on the back. How many such hands consist of a pair of aces?
- Ace then king without replacement ●○○○○ 10 ptsA standard 52-card deck is shuffled. One card is drawn and not replaced, then a second card is drawn. Find the probability that the first card is an ace and the second card is a king. Give your answer as a decimal rounded to four decimal places.
- Ace of spades before face cards ●●○○○ 20 ptsCarson flips over the cards of a standard 52-card deck one at a time. Find the probability that he flips over the ace of spades before any face card (jack, queen or king). Round to two decimal places.
- Aces before the joker ●●○○○ 20 ptsA standard 52-card deck plus one joker (53 cards in total) is shuffled into a uniformly random order and turned over one card at a time. What is the probability that all 4 aces are turned over before the joker? Give your answer as a decimal.
- Aces of spades and clubs adjacent ●●○○○ 20 ptsA standard 52-card deck is shuffled uniformly at random. Find the probability that the ace of spades and the ace of clubs are next to each other in the deck, in either order. Round to four decimal places.
- Each player gets one ace ●●●○○ 50 ptsA deck of 52 cards containing four aces is shuffled thoroughly and the cards are dealt among four players so that each player receives 13 cards. Find the probability that each player receives exactly one ace. Give the answer as a percentage rounded to one decimal place.
- Each player gets an ace ●●●○○ 50 ptsA standard 52-card deck is shuffled and 2 cards are dealt to each of 4 players. Find the probability that every player receives at least one ace. Give your answer as a decimal rounded to eight decimal places.
- One ace per suit in pinochle ●●●○○ 50 ptsA player is dealt a 20-card hand from a double-deck pinochle deck of 80 cards, which contains 4 aces of each suit. Find the probability that the hand contains exactly 1 ace of each of the four suits. Round to four decimal places.
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