1. Suppose that 9 female and 6 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from 15 the finalists, what is the probability of selecting at least 4 females? 2. Your employer gives a grab bag contest for Halloween. The grab bag contains 12 $5 prizes, 6 $25 prizes, and 4 $100 prizes. Three prizes are chosen at random. Find the following probabilities. a. The probability that exactly two $100 prizes are chosen. b. The probability that one of each prize is chosen. C. The probability that at least one $100 prize is chosen. d. The probability that no $5 prizes are chosen. 3. The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt. Wore Seat Belt No Seat Belt Total Driver Survived 416,631 164,824 581,455 Driver Died 467 1867 2334 Total 417,098 166,691 583,789 Find the probability of not wearing a seat belt, given that the driver survived a car accident. 4. The probability of events E, F, EnFare given below. Determine the following. P(E) = -, P(F)= 9, and P(EnF)= 5 a. Determine P( F| E). b. Determine P( E | F' ). 5. In a batch of 25 pedometers, 3 are believed to be defective. A quality-control engineer randomly selects 4 units to test. Let random variable X be the number of defective units that are among the 4 units tested. The probability mass function f(x) = P(X = x) is given below. f(x)=(0,0.57826), (1,0.36522), (2,0.05478), (3,0.00174); The mean u of a discrete random variable X with probability mass function f (x) = P(X = x) is given by u = Ex. . f (x.). a. Find / for the probability mass function above. What does this number represent? b. What is the probability that that at least two pedometers are defective