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# Last two questions before my test tomorrow

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Any help would be appericated. I'm going to see if I can figure out 19.) by myself right now, so I'll update it if I figure it out before someone answers incase anyone else is having trouble with a question like this.

UPDATE - I did them both, I don't know if they are done correctly though.

21.) Interpret the following probability statement into words. Is this an example of mutually exclusive events? Explain.

P(A∪B) = P(A) + P(B) − P(A∩B)

EDIT - The probability of A union B is equivalent to the difference of probability of product of probability of A and probability of B and, the probability of A intersetion B.

19.)

A company has two factories that manufacture light bulbs. Suppose that 55% of the light bulbs are

manufactured in factory A and 45% come from factory B. In factory A 0.7% of the bulbs are defective and in factory B 0.3% of the bulbs are defective. Suppose a defective light bulb is discovered. What is the probability that the defective bulb came from factory B?

EDIT - P(B | defective) = P(B & defective) / P(defective) = 0.135/0.52 = 0.2596 or 25.96%

I think that is correct?

Dec 10, 2017
edited by Guest  Dec 10, 2017
edited by Guest  Dec 10, 2017

#1
+100572
+1

Here's19

Let us suppose that   100000 total bulbs are manufactured by both factories...55000 by A and 45000 by B

So.....the number of defects are   55000 * .007  +  45000  * .003  =    520

So....out of the 520 defects........45000*.003  =  135  come from  B

So.....the probability that a defective bulb comes from  B  given that we have a defective bulb  is just

135 / 520  = .2596

Just as you found  !!!

Dec 11, 2017
#2
+100572
+1

Here's 21

The probability of A union B is equivalent to the sum of  the two separate probabilities  less the product of their probabilities

This will be mutually exclusive whenever  P(A intersect B  )  =   0

Dec 11, 2017