Question

In: Statistics and Probability

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

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 2 years ago

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