If we assume that all possible poker hands (comprised of 5 cards from a standard 52 card deck) are equally likely, what is the probability of being dealt: a. a flush? (A hand is said to be a flush if all 5 cards are of the same suit. Note that this definition means that straight flushes (five cards of the same suit in numeric sequence) are also considered flushes.) b. one pair? (This occurs when the cards have numeric values a, a, b, c, d, where a, b, c, and d are all distinct.) c. two pairs? (This occurs when the cards have numeric values a, a, b, b, c, where a, b and c are all distinct.) d. three of a kind? (This occurs when the cards have numeric values a, a, a, b, c, where a, b and c are all distinct.) e. four of a kind? (This occurs when the cards have numeric values a, a, a, a, b.)

Respuesta :

Answer:

See the attached photo for the calculations and answers

Step-by-step explanation:

The calculations and explanations are shown in the 3 attached photos below.

Ver imagen MrSmoot
Ver imagen MrSmoot
Ver imagen MrSmoot

The answer to the given question will be a) P(flush) = 0.0019 b) P(one pair) = 0.4225 c) P( two pairs) = 0.475 d) P(three of a kind) = 0.211 e) P(four of a kind) = 0.00024

What is probability?

It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.

The probability of being dealt a flush:

For a suit there are 4 choices and 13C₅ choices for a card in that suit

Probability of flush = 4.( 13C₅)/52C₅

Probability of flush = 0.0019

The probability of being dealt one pair:

There are 13 possible values of a, 4C₂ choice for suit of a, 12C₃ value for b, c, d and 4 choices each for choosing the suit of b, c, d.

P(one pair) = (13.4C₂.12C₃.4.4.4)/52C₅

P(one pair) = 0.4225

The probability of being dealt two pairs:

There are 13C₂ possibility for the value of a and b, 4C₂ choices for suits of both a and b and 44 possibilities for c from the remaining cards.

P(2 pairs) = (13C₂.4C₂.4C₂.44)/(52C₅) = 0.475

The probability of being dealt three of a kind:

There are 13 possibilities for the value of a and 4C₃ choices for the suits of a, 12C₂ possibilities for both b and c and 4 choices of suits for both b and c.

P( three of a kind) = (13.4C₃.12C₂.4.4)/52C₅ = 0.211

The probability of being dealt four of a kind:

There are 13 possibilities of a and 4C₄ values for the suit of a and 48 choices of b from the remaining cards.

P(four of a kind) = (13.4C₄.48)/52C₅ = 0.00024

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ2