00:01
In this question, we are given that there is a poker hand which consists of five cards that is dealt with a standard deck of 52 cards.
00:08
We need to find a probability that the hand contains part a is five hearts.
00:12
So for that we first need to know that how many total hearts are there.
00:15
So we know that there are a total of 13 cards which are of hearts.
00:22
So the probability that we have five, all five as hurts, it means that from 13 we choose any five.
00:30
Cards so that's the favorable outcomes over the total outcome is 52c5 so 52c5 means we can we can choose any five cards out of those 52 so 13c5 is 1 287 1 287 over 52 c5 is a big number that's 259 986 so 1 287 over this is coming as a very low value that's coming as 4 .95 times 10 raise 2 minus 4 this is the required value of consist or deck consisting of 5 hearts part b talks about uh five cards of the same suite of the same suite so it can be uh it can be a 13 of hertz it can be 13 of spades it can be 13 of diamonds and it can be 13 of uh uh uh uh uh the other of so heart, diamond, spades, and clubs.
01:34
So it can be 13 of any kind.
01:36
So the probability is going to be either we can have 13 of the, either we can have five for the first, first, first, first suit, or five of second, or five of third or five of fourth.
01:52
Over, we can have the total outcomes are five of any kind.
01:55
That's going to be four times 13 c5 over 52.
02:00
C5 so that's just four times our previous answer that's just four times our previous answer because that's something which we already found so if you multiply that by four we are getting the answer as uh 1 .98 times 10 raised to 9 8 times 10 raise 2 minus 3 so that's the required probability if i want to write this exclusively in decimal so that's going to be 0 .000495 and this exclusively in decimals will be be 0 .00198.
02:38
Okay the part c says that we have five face cards so remember what is a face card for the face card we have ace jack and king we have the a sorry we have the king queen and jack so we have a total of three face cards for once for one such let's call it hurts and for four in total we'll have four times three which is 12 so we have a total of 12 face cards.
03:08
So choosing any five of it will be that because that's what they are saying.
03:13
The all the five are face cards.
03:16
So the probability is going to be choosing any five from these face cards over the total probability which is 52c5.
03:25
So let me find that 12c5 over this.
03:28
So that's coming as 12c5 over this number...