Bayes' theorem?

Question

I don't understand bayes' theorem of probability easily.Please explain this theorem with funny example.

Answer 1

Suppose there are two bowls full of cookies. Bowl #1 has 10 chocolate chip cookies and 30 plain cookies, while bowl #2 has 20 of each. Fred picks a bowl at random, and then picks a cookie at random. We may assume there is no reason to believe Fred treats one bowl differently from another, likewise for the cookies. The cookie turns out to be a plain one. How probable is it that Fred picked it out of bowl #1?

Intuitively, it seems clear that the answer should be more than a half, since there are more plain cookies in bowl #1. The precise answer is given by Bayes's theorem. But first, we can clarify the situation by rephrasing the question to "what’s the probability that Fred picked bowl #1, given that he has a plain cookie?” Thus, to relate to our previous explanation, the event A is that Fred picked bowl #1, and the event B is that Fred picked a plain cookie. To compute Pr(A|B), we first need to know:

Pr(A), or the probability that Fred picked bowl #1 regardless of any other information. Since Fred is treating both bowls equally, it is 0.5.
Pr(B), or the probability of getting a plain cookie regardless of any information on the bowls. In other words, this is the probability of getting a plain cookie from each of the bowls. It is computed as the sum of the probability of getting a plain cookie from a bowl multiplied by the probability of selecting this bowl. We know from the problem statement that the probability of getting a plain cookie from bowl #1 is 0.75, and the probability of getting one from bowl #2 is 0.5, and since Fred is treating both bowls equally the probability of selecting any one of them is 0.5. Thus, the probability of getting a plain cookie overall is 0.75×0.5 + 0.5×0.5 = 0.625.
Pr(B|A), or the probability of getting a plain cookie given that Fred has selected bowl #1. From the problem statement, we know this is 0.75, since 30 out of 40 cookies in bowl #1 are plain.
Given all this information, we can compute the probability of Fred having selected bowl #1 given that he got a plain cookie, as such:


As we expected, it is more than half.

Answer 2

Dist A = 2x Dist B=x assume x=50 Dist A=2(50)=one hundred Dist B=(50)= 50 2% of A are defective variety of computers that are defective from A= 2% of one hundred =2 variety of computers that are defective from B= 4% of fifty = 2 quantity of computers shop has= variety of computers ordered from A + variety of computers ordered from B = one hundred + 50 = a hundred and fifty computers danger of procuring a defective laptop that got here to the shop by way of distributor B = variety of computers that got here from distributor B defective / finished variety of computers interior the shop = 2/a hundred and fifty divide the two by potential of two =a million/seventy 5 or 0.0.33 The e book worked the question by potential of dividing the completed defective computers from distributer B by potential of the completed defective computers interior the shop somewhat of dividing the completed defective computers from distributer B by potential of the completed variety of computers the shop HAS. If I somewhat have achieved what the e book did i might have have been given 2/4, that should offer me 0.5 it somewhat is incorrect

Answer 3

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