00:01
In this question, we have a standard doubt of 52 plain cards in part a.
00:05
Two cards are drawn without replacement.
00:15
We want to find probability both are queens.
00:22
Take note the cards are selected without replacement.
00:28
And there's no mention to after selection whether these two cards are arranged in any special order.
00:35
So the order of selection is not important.
00:40
Without replacement order, not important will be using combination.
00:43
That is ncr.
00:44
So we know that there are four queens in the deck we're going to choose two.
00:52
And probability always divide by the total number of ways in this case of selecting two cards without any restriction.
00:58
They'll be taking from the 52 cards we choose two.
01:03
And so this would be one out of 221 or 0 .0045, 4 decimal place.
01:17
In b, we want to find probability the first card is a 10.
01:25
And the second card is a 5 or 6.
01:33
Now, n is times, set notation is intersect, or is plus, set notation is union.
01:41
So probability first card is a 10.
01:43
We know there are four cards out of 52.
01:48
So this would be the probability of getting a 10.
01:53
There are four cards.
01:54
The number 10 out of 52 cards.
01:57
Now, n is times.
02:00
The second card is 5 or 6.
02:02
We need to consider both together.
02:05
So it's a plus.
02:06
We know there are four cuts with the number five and four cards with number six.
02:11
So total there are eight cuts with the number five or six.
02:14
So in the second round, there will be eight cuts with five or six out of 51 cuts left in the second round because this is without replacement.
02:26
And so this will be eight out of 663 or 0 .0121, 4 .000...