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In: Statistics and Probability

In five-card poker, a straight consists of five cards with adjacent denominations (e.g., 9 of clubs,...

In five-card poker, a straight consists of five cards with adjacent denominations (e.g., 9 of clubs, 10 of hearts, jack of hearts, queen of spades, and king of clubs). Assuming that aces can be high or low, if you are dealt a five-card hand, what is the probability that it will be a straight with high card 8? (Round your answer to six decimal places.)

What is the probability that it will be a straight? (Round your answer to five decimal places.)

What is the probability that it will be a straight flush (all cards in the same suit)? (Round your answer to eight decimal places.)

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Expert Solution

Answer:

Given that:

In five-card poker, a straight consists of five cards with adjacent denominations (e.g., 9 of clubs, 10 of hearts, jack of hearts, queen of spades, and king of clubs)

  if you are dealt a five-card hand, what is the probability that it will be a straight with high card 8

so it is 4,5,6,7,8 of any type from 4

Hence the permutations are =

While the total selection are =

Hence the asked probability =

  P(straight)= Total chances of straight/ chances of taking 5 from 52

So the total flushes can be from ace to 10 with ace,2,3,4,5 till 10,jack,queen,king,ace

Hence the required probability is

Straight flush =

(since now ace to 10 can have 4 colors hence 10*4 numerator and denominator us)

orchestra answered 2 years ago
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