Suppose that A and B are two events for which P(A) = 0.26, P(B) = 0.78, and P(B A) = 0.37. Find each of the following: a) P(An B) = b) P(AU B) = c) P(A | B) =A breathalyser test is used by police in an area to determine whether a driver has an excess of alcohol in their blood (blood alcohol level). The device is not totally reliable: 3 % of drivers with a true blood alcohol level below the legal limit will give a reading from the breathalyser as being above the limit, while 10 % of drivers with a true blood alcohol level above the legal limit will give a reading below the limit. Suppose that in fact '16 % of drivers have a true blood alcohol level above the legal alcohol limit, and the police stop a driver at random. Give answers to the following to four decimal places. Part a) What is the probability that the driver is incorrectly classified as being over the limit (Le. classified as over limit AND has a true blood alcohol level below the limit)? Part D) What is the probability that the driver is correctly classified as being over the limit (i.e. classied as over limit AND has a true blood alcohol level over the limit)? Part c) Find the probability that the driver gives a breathalyser test reading that is over the limit. Part d) Find the probability that the driver has a true blood alcohol level below the legal limit, GIVEN that the breathalyser reading is below the limit. In a packet of candy there are 9 red, 4 green, and 2 blue. a) You pick two candies with replacement. What is the probability that you draw a green followed by a red? P(draw a green then a red) = b) In this example are the events 'green' and 'red' independent? Enter yes or no:Let P(A) = 0.2, P(B) = 0.4, and P(A U B) = 0.6. a) P(AnB) = b) Are events A and B independent? Enter yes or no: c) Are A and B mutually exclusive? Enter yes or no:Find the mean ,u, variance 0' am: (3)0": 2 and standard deviation 0' for the pmf given below: If X is a binomial random variable, compute the following probabilities: a) n = 3, p = 0.2 P(X 3) = c) n = 4, p = 0.4 P(X 1) =A quality-control engineer inspects a random sample of 6 batteries from each lot of 24 car batteries ready to be shipped. If such a lot contains 11 batteries with slight defects, what are the probabilities that the inspector's sample will contain: a) 2 of the batteries with defects? b) 4 of the batteries with defects? A math professor nds that when he schedules an office hour for student help, an average of 3.5 students arrive. Let X be the number of student arrivals in an office hour. Find the probability that in a randomly selected office hour, the number of student arrivals is 1. P{X:1): Suppose that during practice a basketball player can make a free throw 70 percent of the time. Furthermore, assume that a sequence of free-throw shooting can be thought of as independent Bernoulli trials. Let X equal the minimum number of free throws this player must attempt to make a total of 8 shots. X follows a: O A. Geometric Distribution 0 B. Hypergeometric Distribution 0 C. Negative Binomial Distribution. 0 D. Binomial Distribution. If the probability is 0.05 that a certain kind of measuring device will show excessive drift, what is the probability that the 8th measuring device tested will be the first to show excessive drift? P(the 8th device tested will be the first to show excessive drift) =A new medical test has been designed to detect the presence of the mysterious Brainlesserian disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.9. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.1. It is estimated that 11% of the population who take this test have the disease. Let D be the event someone has the disease and P (for positive) the event that the new test detects the disease. If the test administered to an individual is positive, what is the probability that the person actually has the disease? P{D|P) =