00:01
A poker hand consists of five randomly dealt cards from a standard deck of 52.
00:08
The order of the cards does not matter, so we're looking at combinations.
00:12
So the total number of ways that five cards can be drawn is going to be 52 choose five.
00:21
All right, we want to figure out these probabilities rounded to four decimal places.
00:29
All right, so determine the probability that exactly four cards are aces.
00:33
Well, keep in mind there's four aces in our deck.
00:37
That means we want to pick all of them as well the remaining 48 cards.
00:44
We are going to have to have one of that, all right, because we do get five cards in our hand.
00:50
Keep in mind in each of these cases, our denominator is going to be 52 choose five.
00:58
In this case, we wind up with .000184.
01:08
So if we round to the nearest percent, keep in mind it's going to be right here, and we wind up with .0018.
01:24
It was 846, so .0018 percent chance in this case.
01:31
All five of the cards are spades.
01:33
Well, there are 13 spades, so we take 13 choose five and divide by 52 choose five.
01:44
We wind up with this case of .000495198...