i will give 10 points to anyone who can answer this quickly... you have a factor

Question

i will give 10 points to anyone who can answer this quickly...

you have a factory manufacturing objects....
...if the probablility of:
having an error on side of object = 0.02
having an error on top of object = 0.02
having error on side and top = 0.01

then what is the:
a) probability that a random object chosen has no flaw
b) probability that an object has flaw on the top but not on the side
c) probability that there is a flaw on the top, given that there is a flaw on the side

easy problem! can you tackle it? it is all simple conditional probability i.e. P(x|y)

Explanation / Answer

Let A denote having an error on side of object ,B denote having an error on top of object. Given P(A)=0.02 P(A')=1-P(A)=1-0.02=0.98 P(B)=0.02 P(A and B)=0.01 ----------------------------------------------------------------------------------------------- a)P(that a random object chosen has no flaw) =P(A'and B') =1-P(AUB) =1-[P(A)+P(B)-P(A and B)] =1-[0.02+0.02-0.01] =1-0.03 =0.97 ----------------------------------------------------------------------------------------------- b)P(that an object has flaw on the top but not on the side) =P(B and A') =P(B)*P(A') =0.02*0.98 =0.0196 ----------------------------------------------------------------------------------------------- c)P(there is a flaw on the top, given that there is a flaw on the side) =P(B/A) =P(A and B)/P(A) =0.01/0.02 =1/2 --------------------------------------------------------------------------------------------

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