Problem 4 [20 pts]: Playing Cards Let C represent a set of 52 playing cards with...

Problem 4 [20 pts]: Playing Cards Let C represent a set of 52 playing cards with four suits (♥, ♦, ♣, ♠) each having 13 ranks (Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King). We define the following additional sets. F =Face cards (Jack, Queen, and King). R =Red cards. P =Ranks that are prime (2,3,5,7). J =One-eyed Jacks (Jack of Hearts, Jack of Spades).

1. Depict these sets as a Venn Diagram and show the cardinality of each distinct region. (The regions don’t have to be perfectly to scale - this can be hand-drawn.)

2. Using set notation, give an expression for the set of cards that are red or face cards or prime numbered or one-eyed Jacks and give its cardinality.

3. Give a set expression and cardinality for the set of cards that are not face cards or not prime-numbered cards.

4. Give a set expression and cardinality for the complement of the set of cards that are either red or prime-numbered but not one-eyed Jacks.

5. Give a set expression and cardinality for the set of cards that are either red non-prime cards or one-eyed Jacks, but not both.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Assume that a standard deck of 52 playing cards is randomly shuffled (13 cards of 4...

Assume that a standard deck of 52 playing cards is randomly shuffled (13 cards of 4 types of suits - clubs, diamonds, hearts, and spades). If Alex draws a card from it 4 times with replacement, how many different combinations of suits can he get? (Suppose we further assume that the order doesn't matter: (clubs, diamonds, hearts, hearts) is equal to (hearts, clubs, diamonds, hearts). However, (clubs, diamonds, hearts, hearts) is different with (hearts, clubs, clubs, hearts).)

consider a standard deck of playing cards... 52 cards, 4 suits of 13 cards each, 3...

consider a standard deck of playing cards... 52 cards, 4 suits of 13 cards each, 3 cards of each suit are face cards, 2 suits are black (clubs and spades) and 2 are red (hearts and diamond) a) Let event A be drawing a random card that is a diamond. What is a trial for this scenario? What is the sample space? Is A a simple event? What is P(A)? What is A¯, the complement of A? What is P(A¯)?...

4.(4 + 3 marks) In an ordinary deck of 52 playing cards, if a person draws...

4.(4 + 3 marks) In an ordinary deck of 52 playing cards, if a person draws a king or a jack, he is paid $10; if he draws a queen, he is paid $5.If he draws any other card, he will pay $4. a. If X is the gain for the person who plays the game, construct a probability distribution for X. b. Find the expected gain?

A deck of playing cards contains 52 cards, half of which are red cards. What is...

A deck of playing cards contains 52 cards, half of which are red cards. What is the probability that the deal of a five-card hand provides: 1) No red cards? 2) At least 3 red cards? a) .325, .025 b) .325, .5 c) .5, .325 d) .025, .50 e) .5, .15

Two cards are randomly selected from a deck of 52 playing cards. (a) What is the...

Two cards are randomly selected from a deck of 52 playing cards. (a) What is the probability they constitute a pair (that is, that they are of the same denomination)? (b) What is the conditional probability they constitute a pair given that they are of different suits?

Two cards are drawn at random from an ordinary deck of 52 playing cards. If the...

Two cards are drawn at random from an ordinary deck of 52 playing cards. If the two cards display the same suit, you win $2. If they are the same color only, you win $1. Otherwise, you lose 50 cent. Calculate (a) the expected value of the amount you win; (b) the variance of the amount you win;

You draw cards from a standard deck of 52 playing cards. There are 12 “face cards”...

You draw cards from a standard deck of 52 playing cards. There are 12 “face cards” in the deck (J, Q, or K). Let X be the number of drawings (with replacement) it takes until you get your ﬁrst face card. Let Y be the number of drawings (with replacement) it takes until you get your ﬁfth face card. Let Z be the number of face cards removed if you draw 10 cards without replacement. (a) Calculate P(X = 5)....

In a deck of 52 playing cards (A, 2, 3, 4, 5, 6, 7, 8, 9,...

In a deck of 52 playing cards (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K in each four suits), What is the probability of selecting a black (i.e., club or spade) king card? Without replacement means the card IS NOT put back into the deck. What is the probability that when two cards are drawn from a deck of cards without replacement that both of them will be 8’s? What is the probability of being...

You are dealt a hand of five cards from a standard deck of 52 playing cards....

You are dealt a hand of five cards from a standard deck of 52 playing cards. Calculate the probability of the given type of hand. (None of them is a recognized poker hand.) (a) Mixed royal meeting: One of each type or royal card (king, queen, jack, ace) of different suites, and a last non-royal card (neither king, queen, jack or ace). Enter a formula. Examples: C(5,3)C(33,3)/C(14,2) C(5,3)C(33,3)C(4,1)/C(100,100) (b) Red and black double royal wedding: A red king, a red...

You are dealt a hand of five cards from a standard deck of 52 playing cards....

You are dealt a hand of five cards from a standard deck of 52 playing cards. Calculate the probability of the given type of hand. (None of them is a recognized poker hand.) 1. Double royal interracial wedding: Two kings of one color, two queens of the other color, and a last non-royal card (neither king, queen, jack or ace). Solve using a formula. Examples: C(5,3)C(33,3)/C(14,2) or C(5,3)C(33,3)C(4,1)/C(100,100)

Subjects