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. Ac and (A∩cc) 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 ?
23.the number of employees working in factories A,B and C are , respectively 50,75 and 100 . suppose that of those employees ,50% ,60 % and 70%,respectively ,are women .assuming that the probability of resignation is the same for men and women and that woman resigned ,what is the probability that she is from factory c ?
24 . two balanced dice are rolled .if you know that the upper faces show different numbers ,what is the probability that one of the two faces show 4 .