A standard deck of playing cards consists of the four suits (diamond, club, heart, spade) and...

A standard deck of playing cards consists of the four suits (diamond, club, heart, spade) and each suit contains 13 cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King). Suppose ve cards are taken from an ordinary deck of 52 cards. Calculate the following: a) total number of 5-card-combinations b) number of 5-card-combinations where all 5 cards are hearts c) probability that all 5 cards are of the same suite

Solutions

Expert Solution

Total number of cards in the deck = 52

a. Total number of 5-card-combinations

Number of ways of drawing 5 cards from 52 cards =

Total number of 5-card-combinations from 52 cards = 2598960

b) number of 5-card-combinations where all 5 cards are hearts

Number of cards in hearts suit = 13

Number of ways of drawing 5 hearts cards from 13 heart cards =

Number of 5-card-combinations where all 5 cards are hearts = 1287

Probability that all 5 cards are of the same suite = Probability ( that all 5 cards are from Spade suit OR that all 5 cards are from heart suit OR that all 5 cards are from Diamonds OR that all 5 cards are from Clubs) = P(that all 5 cards are from Spade suit) + P(that all 5 cards are from Heart suit) + P(that all 5 cards are from Diamond suit) + P(that all 5 cards are from Club suit)

P(that all 5 cards are from Heart suit) = Number of ways of drawing 5 heart from 13 heart cards / Number of ways of drawing 5 cards from 52 cards

From b). Number of ways of drawing 5 heart from 13 heart cards =1287

From a). Number of ways of drawing 5 cards from 52 cards = 2598960

P(that all 5 cards are from Heart suit) = Number of ways of drawing 5 heart from 13 heart cards / Number of ways of drawing 5 cards from 52 cards = 1287/2598960 = 0.000495

The same applies to the other suites as well,

Therefore

P(that all 5 cards are from Spade suit) = 0.000495

P(that all 5 cards are from Diamond suit) = 0.000495

P(that all 5 cards are from Club suit) = 0.000495

P(that all 5 cards are from Spade suit) + P(that all 5 cards are from Heart suit) + P(that all 5 cards are from Diamond suit) + P(that all 5 cards are from Club suit) = 0.000495+0.000495+0.000495+0.000495 = 0.001981

Probability that all 5 cards are of the same suite = 0.001981

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A standard 52-card deck of French playing cards consists of four suits: hearts, spades, clubs, and...

A standard 52-card deck of French playing cards consists of four suits: hearts, spades, clubs, and diamonds. There are 13 cards of each suit; each suit has cards of rank 2 through 10, along with an ace, king, queen, and jack. Typically, hearts and diamonds are the red suits, while spades and clubs are the black suits. Four cards are drawn from the deck, one at a time, without replacement. a) The second card drawn is from a red suit....

A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each...

A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all. a.) How many 7-card hands will consist of exactly 3 kings and 2 queens? b.) What is the probability of getting a 7-card hand that consists of exactly 3 kings and 2 queens? (Note: Enter your answer as a fraction.)

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¯)?...

An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and...

An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability for a nine, black, not a heart The probability of selecting a nine is: The probability of selecting a black card is: The probability of selecting a card that is not heart is: (type...

Hyram has a standard deck of 52 playing cards. The deck contains 4 suits (hearts, diamonds,...

Hyram has a standard deck of 52 playing cards. The deck contains 4 suits (hearts, diamonds, clubs, and spades), and each suit contains 13 cards labeled 2 through 10, as well as jack, queen, king, and ace. Four friends are trying to determine some probabilities related to randomly drawing a single card from the deck. Consider the following events, and then answer the question. A: drawing a diamond B: drawing a queen Which friend provided the correct analysis? Samantha says...

In a standard deck of 52 cards, there are four suits (clubs, hearts, diamonds and spades)...

In a standard deck of 52 cards, there are four suits (clubs, hearts, diamonds and spades) and 13 cards of each suit. What is the probability of randomly selecting two cards, which turn out to be the same suit? (Answer to 2 digits after the decimal point.)

A deck consists of 72 cards with 9 suits labelled ? to ? and numbered ranks...

A deck consists of 72 cards with 9 suits labelled ? to ? and numbered ranks from 1 to 8. That is, there are 8 cards of each suit and 9 cards of each rank. What is the probability of it being suit C or having rank 6?

The following question involves a standard deck of 52 playing cards. In such a deck of...

The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four...

A deck consists of cards with 5 suits labelled A to E and numbered ranks from...

A deck consists of cards with 5 suits labelled A to E and numbered ranks from 1 to 6 . Each card is equally likely to be drawn. Suits A to C are red. Suits D to E are blue. A card is drawn at random from this deck. 1) What is the probability of it having a rank less than or equal to 2 given it has a rank less than or equal to 3? 2)What is the probability...

A standard poker deck of 52 cards has four suits, (symbols C, H, S, and D)...

A standard poker deck of 52 cards has four suits, (symbols C, H, S, and D) and thirteen ranks (symbols A, 2, 3, 4, 5, 6, 7, 8, 9, T, J, Q, and K). Every card in the deck has both a value and a suit.1 A poker hand is any set of 5 cards from the standard poker deck. There are some special hands in poker, and these have ranks (i.e. some are better, some are worse). From best...

Subjects