00:01
Given this question in the dish, there are eight red, eight blue, and six yellow candies.
00:11
So total number of candies are 22.
00:17
Now, eight candies are selected.
00:20
I'm going to let y be the number of candies out of eight that are yellow.
00:24
Now, take note that the eight candies are selected without replacement.
00:27
So my y actually follows the hypergeometric distribution.
00:37
But i'm going to explain it in another way that's more logical and it's easier for you to understand.
00:44
Now again, i repeat that take note that the eight candies are selected without replacement.
00:56
After they are selected, they are not arranged in any particular order, so order not important.
01:06
So without replacement order not important, we'll be using combination.
01:11
And that's the one we see.
01:14
So we want to find probability at least four candies are yellow.
01:17
So we are looking at probability y greater equals to 4.
01:25
I'm going to take 1 minus the complement to this case would be probability y less than 4.
01:32
So for why less than 4 it can be split into a few mutually exclusive case, the case when y equals to 0, or.
01:41
Now probability n is times or is plus.
01:45
So all, so there's a plus.
01:47
Y equals to 1 or y equals to 2 or y is equal to 3 so for the first case y goes 0 means there are 0 yellow candies so from the red and blue total there are 16 of them so from the red and blue candies 16 of them i'm going to choose 8 choose because we're using combination now in probability you always divide by the total possible ways in this case of choosing eight candies with no restriction.
02:28
They'll be taking from the total 22 sweets or candies we choose eight.
02:35
Okay, for the next case, probability y goes to one means there's one yellow candy.
02:42
So from the six yellow candies, i'm going to choose one.
02:47
N, end is times...