Assume that all (525)poker hands are equally likely. what is the probability that you will be dealt:
(a) a flush (a flush is a hand where all 5 cards are of the same suit)

There is 1.98% of probability of being dealt a flush in 5-card Poker

Step-by-step explanation:

To know the probability of a flush being dealt, we can calculate the number of cases when that happens and divide it by the total number of cases of poker hands that exist, naming A the event of a flush.

We will use combinations (nCr button on a calculator) to count the number of cases, because we don't care about the order (it is the same to be dealt a 2, 4, 6, 7 and 8 of hearts than the opposite order), being a flush the event when we take 5 cards out of 13 of the same suit, times 1 out of 4 possible suits and the total number of cases is taking 5 random cards out of 52.

That means there is about a 2% of probability of being dealt a flush.

In other words, of every 16660 plays, 33 will be, on average, a flush

10 down (bang1)

5 up

5down (2)

2.5 up

2.5 down (3)

1.25 up

1.25 down (4)

now add them up : )

hoped i lol