Bayes' Law is a formula for revising an initial subjective (prior) probability value on the basis of new results, thus obtaining a new (posterior) probability value.
Indicate whether the statement is true or false
Q. 2A pharmaceutical firm has discovered a new diagnostic test for a certain disease that has infected 1 of the population. The firm has announced that 95 of those infected will show a positive test result, while 98 of those not infected will show a negative test result.
a. What proportion of people don't have the disease?
b. What proportion who have the disease test negative?
c. What proportion of those who don't have the disease test positive?
d. What proportion of test results are incorrect?
e. What proportion of test results are correct?
Q. 3Is it possible to have two events for which P(A) = 0.40, P(B) = 0.50, and P(A or B) = 0.30? Explain.
Q. 4Suppose P(A) = 0.30, P(B) = 0.50, and P(BA) = 0.60.
a. Find P(A and B).
b. Find P(A or B).
c. Find P(AB).
Q. 5Suppose A and B are two mutually exclusive events for which P(A) = 0.30 and P(B) = 0.40.
a. Find P(A and B).
b. Find P(A or B).
c. Are A and B independent events? Explain using probabilities.
Q. 6A survey of a magazine's subscribers indicates that 50 own a house, 80 own a car, and 90 of the homeowners also own a car. What proportion of subscribers:
a. own both a car and a house?
b. own a car or a house, or both?
c. own neither a car nor a house?
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