00:01
This is a probability question.
00:02
So for a deck of 52 cards, we have 52 cards.
00:07
So the sample space here, which is equal to 52.
00:10
And the number of heard, so the number of heard, which is 13 here.
00:17
So for part a, what is the problem that the first card? so i'm going to just throw second cards, i mean two cards.
00:24
Let's say this is the first and this is the second.
00:27
So the probability of getting the first card is heard, which is 3.
00:30
13 over 52, but the operation has not ended.
00:34
I'm going to just keep multiplying.
00:36
And the second one is not.
00:37
So this is without replacement.
00:39
So that means there are 51 cards remaining here.
00:42
And i just use one of them, which is 12 hertz remaining here.
00:47
And what about the total remaining card, which is not heard? so that means this is 39.
00:53
So from this step, i can just multiply these two, which is 13 times.
00:59
Sorry this is 13 times 39 and this is divided by open the bracket this is 52 times 51 so the answer would be 0 .19 and 12 and what about for part b the problem that the second card is not heard so the problem that the second card is not heard so that means the first card would be heard and the second card not heard or the first card would be heard and the second card would be also hurt here let me just write as heard so the probability of first card is heard which is 13 over 52 and not hurt this is 39 over 51 and plus so the both of them would be the hurts which is 13 over 52 and times this is 12 over 59 let me get this one here so i'm going to just multiply this is 13 times, this is 13 times, which is 12.
02:08
And this is divided by which is, let me just open the bracket, this is 52 times 51.
02:14
So the probability would be which is 0 .1912 and plus 0 .0588, which is, let me just get this number here and plus the other number we got.
02:27
So the probability would be 0 .25.
02:30
And what about for part c? first one is heard what is the problem that the second second one is not heard so probability of getting the first card is heard which is one and this is 13 over 52 and the second one is not heard which is 39 over 51 which is the same as the power of a so this probability is equal to 0 .19 and 12 and what about the if the first card is spade so when we look at the number of spade here for party the first card is spade so the number of spade so the number of spade card here which is equal to 13 and the number of a's which is equal to full and their intersection the spade intersect let me just write as at and a's which is equal to one here so if the first card is spayed so there should be two probabilities the first one the first one should be the spade ace and the next one is also which is an ace so this is the probability of ace or plus the probability of spade this is spade not ace and ace so the probability of the first one is spade a is which is um this is one over 52 and times the next one is there are the remaining three here that should be which is three over um and 51 and plus the next one this is not ace um so the number of spade which is not ace this is 12 over 52 and times the next one is ace so we have total of four a's which is 51 here let me get this one here this is uh which is equal to 1 .3 plus 12 times 4 and divided by 52 times 51.
04:31
So this is equal to 51 over 52 times 51.
04:37
If i simplify, this is 1 over 52.
04:39
This is the probability we have for this case here.
04:43
And what about the next one? so we have to write for the last part the probabilities here.
04:49
Let's say this is the first drawn card and this is the second one here.
04:53
So what we want? we want the their combined value is between 10 and 16.
04:59
So when we look at the deck of cards, so we have the numbers from 2 up to 10.
05:07
First of all, we can just write the values for the numbers.
05:12
And when we look at this case, write the probabilities.
05:15
So the first card would be in the number 2.
05:18
And the next one would be if it is 10, that would be 8, 9, and 10.
05:24
Also that would be so we know that the jack queen king have the value of 10 so this is jack which is queen and the king and the ace that would be ace and what about for the first card is three so that would be seven which is this is eight nine and ten so this is jack queen king and the ace if it is four that would be which is 7, not 7, this is 6, 8, 9, 10, jack, queen, king and ace.
06:05
And it is 5, so this is 5, 6, 7, 8, 9, 10, and then jack, queen, king and ace.
06:17
If it is 6, that would be, which is 4, 5, 6, 7, 8, 9 and 10.
06:25
This is jack, queen and king, not ace.
06:30
And with about seven, this is three, four, five, six, seven, eight, nine, ten...