Question

6. Pollution of the rivers in the United States has been a problenm for many years. Consider the following events: A: the river is polluted, B: a sample of water tested detects pollution C: fishing is permitted. Assume P(A) PlB | A,) 0.3. P(B1A)-0.75, 0.20. P(C' | A n B)-0.20. P(CIA, n B) 0.15. P(CI A'n B)-0.90. P(C | A n B')-0.80. (a) Find P(AnBnc. (b) Find P(B'nc. (c) Find the probability that the river is polluted. given that fishing is permitted and the sample tested did not detect pollution, i.e. find P(A CnB) (d) Suppose A and B are the only 2 events in the problem (so completely ignore event C for this part). Find P(A B). 7. Let C' represent the event that a person has cancer, Let D represent the event that a person is diagnosed with cancer. In a certain region of the country it is known from past experience that the probability of selecting an adult over 40 years of age with cancer is 0.08. The probability of a doctor correctly diagnosing a person with caucer as having the clisense 1S P(D C) 0.84, and the probability of incorrectly diagnosing a person without cancer as having the disease is P(D (*)-0.01. Wliat is the probability that a person diagnosed as having cancer actually has the disease, ie. find P(C D)? Round all values to I decimals. if needed

6&7

Answer 1