00:01
In the asked question an urn, an earl contains 3 green, 1 red and 2 blue balls again 3 green 1 red 2 blue balls 2 balls are taken from the urn 1 after the other and without replacement we will take 2 without replacement it's required to find the conditional probability that the first ball selected was blue first was blue given that second bullet selected was not blue.
00:41
Second was not blue.
00:50
How we can find this probability? we can find that using many ways.
00:57
One way is directly to use the conditional probability rule and another way is to use the probability tree.
01:06
I'll use the two approaches here.
01:09
Let's first find this probability using the conditional probability rule.
01:17
It is the probability of the intersection between two events, which means the first is blue, then the second is not blue.
01:28
We can denote not blue as event n and event b to be blue.
01:37
Then it's blue followed by not blue.
01:44
Divided by the probability of the conditioning event.
01:49
Here, the conditioning event is second.
01:54
Is not blue or is n.
02:02
The denominator is easy to calculate.
02:05
It is the probability of first is blue, first is blue, multiplied by the probability of second is not blue, given that the first is blue...