a) What is the chance that both are blue? _________

Q. Recall that a standard 52-card deck has 4 suits, namely ♥, ♦, ♣, and ♠, each of which has 13 cards of different kinds or ranks, namely A, K, Q, J, 10, 9, 8, 7, 6, 5, 4, 3, and 2.One infamous five-card hand is the Dead Man’s Hand, consisting of A♣, A♠, 8♣, 8♠, and Q♥. According to legend – there seem to be no contemporary accounts that describe the hand – this is the poker hand that James Butler “Wild Bill” Hickok held when he was shot in the back of the head in a saloon in the town of Deadwood in the then Dakota Territory in 1876.1. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will be the Dead Man’s Hand? 2. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will have no card in common with the Dead Man’s Hand? 3. If you draw a five-card hand at random and all at once (so order doesn’t matter), what is the probability that it will have exactly one card…

A standard deck of cards has 52 cards in four suits: spades, hearts, diamonds, and clubs. Spades and clubs are black; hearts and diamonds are red. Each suit has 13 cards: 2 through 10, Jack, Queen, King, Ace. The "face cards" are the Jack, Queen, and King. Robby Billity shuffles a standard deck and draws one card. Then Robby Replaces the card, shuffles again, and draws another card. He repeats this procedure for a total of 1000 draws. About how many times would we expect Robby to draw these cards?  A) the ace of spades B) a face card in any suit

You are given a deck of n cards, which are numbered 1 through n. After the n cards are randomly shuffled, the cards are dealt face up on the table, one card at a time. Here are the rules of NALGO: after the first card is placed on the table, each new card must have a higher number than the previous card. If it does, this new card remains on the table. If the new card is lower in value, then this card is removed from the table and the game is immediately over. Your final score is the number of cards that are placed on the table. For example, if n = 3, then there are six possible scenarios, each of them equally likely to occur. The cards placed on the table are marked in bold. First Card Second Card Third Card 1 2 3 1 3 2 2 2 3 3 1 3 1 2 3 1 2 1 Cards on Table 1, 2, 3 1, 3 2 2, 3 3 3 Points 3 2 1 2 1 1 Thus, if there are n = 3 cards in the deck, then you score 1 point with probability , 2 points with probability, and the maximum 3 points with probability. And so, the expected value of…

You are given a deck of n cards, which are numbered 1 through n. After the n cards are randomly shuffled, the cards are dealt face up on the table, one card at a time. Card rule: after the first card is placed on the table, each new card must have a higher number than the previous card. If it does, this new card remains on the table. If the new card is lower in value, then this card is removed from the table and the game is immediately over. ***The image is the example*** Questions: Prove that for all positive integers n ≥ 3, if there are n cards in the deck, you score exactly 1 point with probability 12 and exactly 2 points with probability 13.

15) Use the situation below to answer the question that follows. Team Jet has 7 members who won a school competition. Of these 7, 4 members are randomly picked to receive prizes for winning. The 1st member selected wins a $50 gift card; the 2nd person selected wins a $25 gift card; the 3rd person selected wins a $10 gift card; the 4th person selected wins a $5 gift card. The names of Team Jet's members are represented by the first letter of their first names, as displayed in the following table: Name Frank Gina Harriet Inez Jakob Keven Liu Letter F G H I J K L In the box below, complete the remaining three rows of the list that models how to calculate the number of possible ways 4 team members can be selected to win the prizes. 1) FGHIJKL Let Lui win the 1st prize, so select L. 2) 3) 4)