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 10? what is the probability that it will be a straight? what is the probability that it will be a straight flush (all cards in the same suit)?

a) 0.000394

b) 0.0256

c) 0.00002

Step-by-step explanation:

There are C(52,5) ways of selecting 5 cards from a deck of 52, where C(52,5) is combinations of 52 taken 5 at a time.

a)

There are only four cards ten. Once you have selected a ten, there are only 4 cards 9, 4 cards 8 and so on.

By the principle of counting (rule of product), there are 4*4*4*4*4= 1024 ways of having a straight with a higher card 10. So, the probability of this event is

1,024/2,598,960 = 0.000394

b)

There are 52 ways of choosing a random card. Once that card is chosen, it could be the 1st, 2nd ,3rd ,4th or 5th in the straight.

For each of this possibilities,since poker cards have 4 different kinds, by the rule of product, there are  

possibles straights, so there are ways of having a straight. The probability of a 5-card straight is

c)

There are only 52 ways of being dealt a straight flush, so the probability of this rare event is

52/2,598,960 = 0.00002

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent