Question

The chances of defective screws in three boxes A, B and C are 1/5, 1/6 and 1/7, respectively. A box is selected at random and a screw drawn from it at random is found to be defective . Then, find the probability that it came from box A.
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Answer 1

Step-by-step explanation:

Given Rani feels that if she earns a profit of set 40 at this craft fair,hee business will be successful enough for her branch out to other craft fair.  How many ornaments does she have to sell to earn a set 40 profit?

By combining $ 40 profit and $ 30

Given The chances of defective screws in three boxes A, B and C are 1/5, 1/6 and 1/7, respectively. A box is selected at random and a screw drawn from it at random is found to be defective . Then, find the probability that it came from box A.

Let E1 E2 and E3 are events of selecting box A, B and C respectively.

So probability will be P (E 1) = 1/3 , P (E2) = 1/3 and P (E3) = 1/3

Now assume A to be customly selected screw is defective. By Baye’s theorem we get

P (E1 / A) = P(E1) x P (A / E1) / P(E1) x P (A/E) + P(E2) x P (A/E2) + P (E3) x P (A/E3)

So P(A / E1) = 1/5, P (A / E2) = 1/6, P (A/E3) = 1/7

P (E1/A) = 1/3 x 1/5 / 1/3 x 1/5 + 1/3 x 1/6 + 1/3 x 1/7

             = 42 / 107