Qatar University, College of Engineering GENG 200 Assignment # 1 Due date: March. 7, 2016 (1) (10 Marks) A car orders are summarized by the optional features that are requested as follows: Proportion of orders No optional features 0.15 One optional feature 0.35 Two optional features More than two options 0.15 0.35 (a) What is the probability that an order requests at least two optional features? (b) What is the probability that an order does not request more than two features? (2) (30 Marks) Wires from a manufacturer are analyzed for conductivity and strength. The results from 100 wires are as follows: Strength High (HS) Low (LS) High Conductivity (HC) 60 18 Low Conductivity (LC) 10 12 (a) If a wire is randomly selected, what is the probability that its conductivity is low and its strength is high? (b) If a wire is randomly selected, what is the probability that its conductivity is low or strength is low? (c) Consider the event that a wire has a high conductivity and the event that the wire has a high strength. Are these two events mutually exclusive? (d) Consider the case where two wires are selected without replacement. What is the sample space for this experiment? (Hint, for instant one outcome can be as (HC1,HS1,LC2,LS2) which implies that the first wire has HC and HS and the second wire has LC and LS. (e) In the case (d), what is the probability of the outcome (HC1,HS1,HC2,HS2)? (f) In the case (d), what is the probability that the second wire has low conductivity and low strength given that the first wire has high conductivity and low strength. (3) (30 Marks) A batch of 300 samples of containers for frozen apple juice contains 20 that are defective. Three samples are selected at random, without replacement from the batch. (a) Identify the sample space S for this experiment. (b) What is the probability that the first one selected is not defective and the second and third samples are defective? (c) What is the probability that the second one selected is not defective given that the first one was defective? (d) What is the probability that the second and third samples are defective knowing that the first one is defective? (e) What is the probability that all three are defective? (f) What is the probability that all three are acceptable? (4) (15 Marks) In a presidential election, exit polls from Washington State provided the following results. John Bush Not employee (65%) 32% 68% Employee (35%) 61% 39% a) (10 Marks) If a randomly selected respondent voted for Bush, what is the probability that the person is not an employee? b) (5 Marks) If a randomly selected respondent was not an employee, what is the probability that the person has votes for Bush? (5) (15 Marks) A company producing electric relays has three manufacturing plants producing 50, 30 and 20 percent, respectively, of its product. Suppose the plants are independent and the probabilities that a relay manufactured by these plants is defective are summarized in the following table: Plant number Probability of defectiveness of the relay Plant 1 0.02 Plant 2 0.05 Plant 3 0.01 (a) If a relay is selected at random from the output of the company, what is the probability that is not defective? (b) If a relay selected at random is found to be not defective, what is the probability that it is manufactured by plant 2?