00:01
The scenario for this question is we have three coins in a box.
00:05
One is a two -headed coin.
00:07
So that means the probability of getting heads, given that it's coin one, is one, because the two -headed coin is always going to show heads.
00:17
The second coin is a fair coin.
00:19
And so the probability of getting heads, given that you're using the second coin, is one -half.
00:26
And the third coin is a biased coin, such that it gets heads 75 % of the time.
00:32
So the probability of heads, given that it's the third coin, is 3 out of 4.
00:39
One of the coins is selected and flipped at random, and it shows heads.
00:45
So what is the probability that it was the two -headed coin? so what is the probability that it was the first coin? so mathematically, we write this conditional probability like this.
00:56
Probability that it was coin 1, the two -headed coin, the two -headed coin, given that we got heads.
01:06
Now to solve this problem, we can make use of beez's theorem, and beez's theorem basically says the following.
01:17
The probability of b given a is equal to the probability of a given b times the probability of b over the probability of a...