Suppose we are given three boxes, Box A contains 10 light bulbs, of which 4 are defective, Box B contains 6 light bulbs, of which 1 is defective and Box C contains 8 light bulbs, of which 3 are defective. We select a box at random and then draw a light bulb from that box at random.   What is the probability that the bulb is defective?  Hint: Here we are performing two experiments:     a) Selecting a box at random           b) Selecting a bulb at random from the chosen box

1. In the casino game Roulette, a bet on “red” will win if the ball lands on one of the 18 red numbers of the 38 numbers on the wheel, with each number being equally likely. You want to run a simulation that will estimate the probability of a player winning both bets when betting on red twice. Which of the following would be an appropriate setup for the simulation: I. Use a table of random digits to select one number from 01 to 38 and then a second number from 01 to 38. If the first number is between 01 and 18 and the second number is between 01 and 18, then the player has won both rounds.  II. Use a table of random digits to select two numbers 01-38, without repeats. If both numbers are between 01 and 18, then the player has won both rounds. III. Use a table of random digits to select two numbers 01-19, allowing repeats. If both numbers are between 01 and 09, then the player has won both rounds.  (A) I (B) II (C) III (D) I and II (E) I and III

A manufacturer obtains clock - radios from three different subcontractors: 40% from A, 30% from B, and 30% from C. The defective rates for these subcontractors are 5 %, 4 %, and 1% respectively. If a defective clock - radio is returned by a customer, what is the probability that it came from subcontractor A? From B? From C?

Question 3: A package is being delivered to your home by one of the following shipping carriers: Postal Service, FedEx, or UPS. Suppose 40% of all packages are shipped by the Postal Service, 25% are shipped by FedEx, and 35% are shipped by UPS. The probability of the package being lost by these shipping carriers is 5%, 3%, and 7%, respectively. a) What is the probability that your package is lost? b) Given your package is lost, what is the probability that it was shipped by UPS?