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)

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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

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orchestra answered 1 year ago

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