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lions [1.4K]
3 years ago
7

In five-card poker, a straight consists of five cards with adjacent denominations (e.g., 9 of clubs, 10 of hearts, jack of heart

s, 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.)
Mathematics
1 answer:
GREYUIT [131]3 years ago
5 0

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

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