Thread: questions need answers

20. if (A∩B∩C)≠0 and P(C|A∩B)=P(C|B) , show that : P(A|B∩C)=P(A|B)

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21 . suppose that A,B and c are independent events .show that
i. A and (A∩B) are independent.
ii. A and (AUB) are independent.
iii. A^c and (A∩c^c) are independent.

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22. in a city ,25% of the cars emit pollutions to the air of the city .if a car failed to pass the emission of air pollutants with probability 0.99 and if a car that is not emitting air pollutants also fails the test with probability 0.17 .what is the probability that a car that fails the test actually emits air pollution ?

Originally Posted by compufatwa

20. if (A∩B∩C)≠0 and P(C|A∩B)=P(C|B) , show that : P(A|B∩C)=P(A|B)

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Originally Posted by compufatwa

21 . suppose that A,B and c are independent events .show that
i. A and (A∩B) are independent.
ii. A and (AUB) are independent.
iii. A^c and (A∩c^c) are independent.

To show independence, we need to show that

so,
i)

im not sure with it (i.e. if A is independent to itsefl)..
just do the same thing with the others
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