Question

In: Statistics and Probability

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)

Solutions

Expert Solution

Answer:-

Given That:-

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)

Given,

Total number of cards = 52

any 5 cards can be chosen in ways =

= 2598960

One colour can be chosen in

Number of kings are quuens in selected color (2 + 2) = 4

The number of ways 2 kings or 2 queens of one color can be chosen in ways

Number of non-royal cards of the remaining colour = (9 + 9) = 18

2 non royal cards at the remainaing colours can be chosen in

= 18!/(2! * 16!)

= 153

Remaining non royal denomination = (9 - 2)

= 7

5Th cards can be chosen = ways

= 7

Required probability =

= 0.0016

Thank you for your supporting. Please upvote my answer...

orchestra answered 1 year ago
Next > < Previous

Related Solutions

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...
A hand of 13 cards is dealt from a standard deck of 52 playing cards. What...
A hand of 13 cards is dealt from a standard deck of 52 playing cards. What is the probability that it contains more spades (♠) than hearts (♡) given that the hand contains at least two spades?
A five-card poker hand dealt from a standard 52-card deck of playing cards is called a...
A five-card poker hand dealt from a standard 52-card deck of playing cards is called a three-of-a-kind hand if it contains exactly three cards of the same rank (e.g. 3 aces and 2 other cards). How many distinct three-of-a-kind hands can be dealt with? Calculate a numeric answer.
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards....
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places. Determine the probability that exactly 3 of these cards are Aces. Answer:  % Determine the probability that all five of these cards are Spades. Answer:  % Determine the probability that exactly 3 of these cards are face cards....
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards....
A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places. Determine the probability that exactly 3 of these cards are Aces. Answer: % Determine the probability that all five of these cards are Spades. Answer: % Determine the probability that exactly 3 of these cards are...
A) A poker hand consists of five cards randomly dealt from a standard deck of 52...
A) A poker hand consists of five cards randomly dealt from a standard deck of 52 cards. The order of the cards does not matter. Determine the following probabilities for a 5-card poker hand. Write your answers in percent form, rounded to 4 decimal places. Determine the probability that exactly 3 of these cards are Aces. Answer: % Determine the probability that all five of these cards are Spades. Answer: % Determine the probability that exactly 3 of these cards...
A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards....
A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four cards of one suit and one card of another​ suit?
1. Five cards are dealt at random from a well-shuffled deck of 52 playing cards. Find...
1. Five cards are dealt at random from a well-shuffled deck of 52 playing cards. Find the probability that: a. All are spades. b. Exactly two are hearts. c. Exactly three are clubs. d. All are red. e. At least one card is ace. 2. Tossing a coin 15 times find the probability of getting exactly 4 tails. 3. Find the probability of getting at least 4 tails for tossing a coin 15 times
A bridge hand consists of 13 randomly-dealt cards from a standard deck of 52 cards. What...
A bridge hand consists of 13 randomly-dealt cards from a standard deck of 52 cards. What is the probability that, in a randomly-dealt bridge hand, there is no card that is a ten or higher? (By ten or higher we mean that a card is either a ten, a jack, a queen, a king, or an ace.)
Assume that 5 cards are dealt at random from a standard deck of 52 cards (there...
Assume that 5 cards are dealt at random from a standard deck of 52 cards (there are 4 suits in the deck and 13 different values (ranks) per each suit). We refer to these 5 cards as a hand in the rest of this problem. Calculate the probability of each of the following events when dealing a 5-card hand at random. (a) Exactly one pair: This occurs when the cards have numeric values a, a, b, c, d, where a,...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT