132 4. A study was conducted in 1997 to measure the total fat content, calories, and sodium content of vegetable burgers available at supermarkets and commonly used as a meat substitute. Measure- ments on 54 different brands of "veggie burgers," and the results were used to develop the 3-way contingency table below. 130 Calories or More Under 130 Calories 320 g Sodium or More Total Fat Under 320 g Under 320 g 320 g Sodium or More Content Sodium Sodium Under 3 g 3 - 4 g Over 4 g 6. 12 3. 6. Total Fat"} %3D onder 130 Calories"}, B = {«320 g Sodium or More" }, C = {“Over 4 g %3D A vegetable burger is selected randomly from the group. Find the following probabilities: (a) P(A) (b) P(B) (c) P(C) (d) P(An B) (e) P(AN BNC) (f) P(AU B) . A certain stretch of highway on the New Jersey Turnpike has a posted speed limit of 60 mph. A survey of drivers on this portion of the turnpike revealed the following facts: • 18% of the drivers were female • 89% of the drivers were exceeding the speed limit by at least 5 mph (and subject to being stopped) • Of those speeding, 15% of the drivers were female (a) Using F for female and S for speeding, convert each of the bullets above into probability statements. (b) Find the probability that a driver on this stretch of highway is female and exceeding the speed limit. (c) Given a driver on this stretch of highway is female, what is the probability that the driver is speeding? (d) Given that a driver on this stretch of highway speeding, what is the probability that the driver is male? (e) For this stretch of highway, are being female and exceeding the speed limit independent or dependent events? Explain using probabilities. (f) For this stretch of highway, are being female and exceeding the speed limit mutually exclusive (disjoint) events? Explain using probabilities. 6. Suppose we deal three cards from a regular deck of cards without replacement. What is the probability of successively drawing an Ace, a King, and a Queen?