Question

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 9? (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.)

Answer 1

1)if you are dealt a five-card hand, what is the probability that it will be a straight with high card 9

so it is 5,6,7,8,9 of any type from 4

Hence the permutations are = 4^5

While the total selection are = 52C5

Hence the asked probability = 4^5/52C5

=0.0003940038

=0.000394 (6 decimals)

2) 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

=(4^5)*10/(52C5)

=0.00394 (5 decimals)

3) Straight flush = 10*4/52C5 (since now ace to 10 can have 4 colors hence 10*4 numerator and denominator us 52C5)

=0.00001539

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!