00:01
Hi, i'm david and i'm here to have you answer your question.
00:04
Now let me bring up your question here.
00:06
In this question we will discuss about the binomial distribution.
00:10
And here, let me remind you that you have x followed by the binomial with the n and b.
00:18
Then the probability of the x equal to k, it will equal to n choose k, b power k, 1 minus b b b b b, minus k.
00:27
Now in this question here, we're given that the bias con land the head with the probability of the b, and it will flip under 10 times, so n equal to 10 and b equal to b.
00:42
And then given that a total 6 hat result, and then we have the total number on the hat in the 10 flips, it will equal to the 6.
00:55
And then i'm going to find the conditional probability a here, that the first three outcomes are on the form, hat, tail, and tail.
01:09
And given that, we will have the number of the six, number of the hat in the ten flips equal to the six.
01:18
Now, by the conditional probability, this one will equal to the probability of the hat, tau, tell, intersection of the number of the head in the 6 in the 10 flip will equal to the 6 divided by probability that the number of the head in the in the 10 flip will be equal to the 6 now we know that for the bottom 1 it will be computed by the i will recall the x equal to the number of the hat in 10 flips and then x followed by the binomial when the n equals to the 10 b it will equal to the b so therefore want to find the proper number of the head it will equal to 6 it will be the same as the probability x equal to the 6 if we apply the formula here we should get it will equal to the 10 to 6 and then b power 6 and then 1 minus b power 10 minus 6 will be 4 that will be the value in the denominator so 10 to 6 and then b power 6 1 minus b power 4 now for the top 1 now we know that there are 6 head and then we will have already one head above 1 here so it means that we will have now to get the first one will be hat, it will be the b.
03:01
The second tail will be the 1 minus b.
03:04
The second one will be 10 will be 1 minus b square.
03:09
And the rest of the seven flips after that we will have the seven flipped afterward.
03:20
It will consist of the five half.
03:26
And then two tails so this means that will equal to the probability on the x it will equal to the i will call this one will be the y now so why it will equal to the binomial now and equal to seven only and then b equal to p so this one will be probability y equal to the five so therefore we should have here will be the seven we choose five b power 5 and then 1 minus b power of the 2.
04:00
So that will be the one on the top.
04:02
We have to multiply extra here, 7 choose 5.
04:06
And then b power 5, 1 minus b power 2.
04:11
So if we simplify everything, we see that we have b power 6 will be cancelled out.
04:19
B power 4 will be cancelled out.
04:22
So we have left with only the 7 choose 5.
04:26
Dividing by the 10 to 6...