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.)

Answer 1

Answer:

$0.000394$

Step-by-step explanation:

First we will find the probability of selecting five cards out of pack of cards

Probability of selecting five cards is equal to

$^{52}C_5$

On expanding we get

$\frac{52!}{47! * 5!}$

$\frac{52 * 51 * 50 * 49 * 48 * 47!}{47 ! * 5*4*3*2*1} \\= 2598960$

straight high card $9$ means five cards with values lesser than $9$ but adjacent to it are

$9, 8, 7, 6, 5$

there are four card for each number

Hence, probability of choosing five cards is equal to

$4*4*4*4*4\\= 1024$

Probability of getting a straight with high card 9 is equal to

$\frac{1024}{2598960}$

$0.000394$