This problem is based on the principle of conditional probability and application of baye's theorem:-
7. Let C represent the event that a person has cancer. Let D represent the event...
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 pasit 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 cancer as having the disease is P(D C) 0.84, and the probability of incorrectly diagnosing a person without...
6&7
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...
In a certain region, the probability of selecting an adult over 40 years of age with a certain disease is 0.03 If the probability of correctly diagnosing a person with this disease as having the disease is 0.90 and the probability of incorrectly diagnosing a person without the disease as having the disease is 0.01, what is the probability that an adult over 40 years of age is diagnosed with the disease?
Let D be the event that a randomly chosen person has seen a dermatologist. Let S be the event that a randomly chosen person has had surgery for skin cancer. Identify the answer which expresses the following with correct notation: The probability that a randomly chosen person has had surgery for skin cancer, given that the person has seen a dermatologist. Select the correct answer below: P(D|S) P(D AND S) P(S) AND P(D) P(S|D)
(XI suppose in a certain population, 8% of all adults over 50 have diabetes. If a community health service in this population correctly diagnoses 95% of all persons with diabetes as having the disease and incorrectly diagnoses 1% of all persons without diabetes as having the disease, find the probability that a) the community health service will diagnose an adult over 50 as having diabetes. b) a person over 50 diagnosed by the health service as having diabetes actually has...
Two doctors independently examine a person randomly chosen from a certain population to check for the presence or absence of a particular disease. Let CA be the event that Doctor A makes the correct diagnosis, CB the event that Doctor B makes the correct diagnosis, and D the event that the randomly chosen patient actually has the disease in question. The doctors are equally skilled, so we have P(CAD) = P(CB|D) = pi and P(CA|DC) = P(CB|DC) = po Finally,...
Let E be the event that a randomly chosen person exercises. Let D be the event that a randomly chosen person is on a diet. Identify the answer which expresses the following with correct notation: Of all the people who exercise, the probability that a randomly chosen person is on a diet. Select the correct answer below: P(D) AND P(E) P(E AND D) P(E|D) P(D|E)
Let the set J represent the event that Joe hits the target and S the event that Sam hits the target. a) In the box, represent the sample space of outcomes as a Venn diagram. Show all of the outcomes and the probabilities on your Venn diagram. Describe in words the event represented by the set JnS.Write down the value of P(Jns) b) c) Describe in words the event represented by the setJnS".Shade the space on your Venn diagram that...
Let C be the event that a computer crashed and O the event that a computer overheated. Suppose we have the following probabilities: P(C)=0.4 P(C∩O)=0.25 P(C′ ∩O)=0.05P(O)=0.3 P(C∩O′)=0.15 P(C′ ∩O′)=0.55 Answer the questions below. Round your answers below to 2 decimals. (a) Find the probability that the computer crashed, given that the computer overheated. (b) Find the probability that the computer crashed, given that the computer did not overheat. (c) Find the probability that the computer did not overheat, given...
1&2
· Let e be the event that a computer crashed and O the event that a computer overheated Suppose we have the following probabilities: P(C) 0.4 P(Cno) 0.25 P(O) 0.3 P(C no) 0.05 )-0.15 P(C no) 0.55 Answer the questions below. Round your answers below to 2 decimals. (a) Find the probability that the computer crashed, given that the computer overheated. (b) Find the probability that the computer crashed, given that the computer did not (c) Find the probability...