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

--------------------------------------------------------------------------

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.

-----------------------------------------------------------------------

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 ?