1. Given the probabilities in the table below for events in a sample space S, find the following probabilities. A B C D Totals E 0.02 0.08 0.06 0.04 0.2 F 0.05 0.1 0.3 0.35 0.8 Totals 0.07 0.18 0.36 0.39 1.00 1.1 P(B) 1.2 P(A ? F) 1.3 P(D | E) 1.4 P(C | C) 2. Refer to the following experiment: 2 balls are drawn in succession out of a box containing 2 red and 5 white balls. Let Ri be the event that the i th ball is red, and let Wi be the event that the i th ball is white. Construct a probability tree for this experiment and find the probability of each of the events R1 ? R2, R1 ? W2, W1 ? R2, W1 ? W2, given that the first ball drawn was 2.1 Replaced before the second draw 2.2 Not replaced before the second draw 3. Find the probabilities by referring to the following tree diagram and using Bayes' formula. 3.1 P(B | F) 3.2 P(A | E) 3.3 P(C | D)

3.4 P(C | F) 4. The following table gives the probability distribution of the number of flights that are overbooked per day for Boston Airlines. Number of Flights Overbooked 0 1 2 3 4 Probability 0.2 0.2 0.4 0.1 0.1 4.1 Find the expected number of flights that are overbooked per day. 4.2 What is the standard deviation in the number of flights that are overbooked per day? 5. Use the following data for this question. Car Miles per gallon (MPG) 2017 AUDI A4 37 2017 AUDI A3 35 2017 AUDI A6 34 2017 BMW 320I 35 2017 BMW 530I 33 2017 BMW 330I 34 2017 LEXUS ES300 39 2017 LEXUS CT200 40 2017 LEXUS GS450 34 2017 VOLVO S60 36 2017 VOLVO S90 34 Find the mean, median, and mode for the data. 6. A pharmaceutical laboratory claims that a drug causes serious side effects in 20 people out of 1,000, on average. To check this claim, a hospital administers the drug to 10 randomly chosen patients and finds that 3 suffer from serious side effects. 6.1 If the laboratory's claims are correct, what is the probability that the hospital gets these results? 6.2 If a hospital administers the drug to 10 randomly chosen patients and finds that more than 1 suffer from serious side effects, what is the probability that the hospital gets these results? 7. A certain brand of lightbulb has a lifetime expectancy that is approximately normally distributed. The mean is 900 hours with standard deviation of 75 hours. What is the probability that a lightbulb will work for 7.1 more than 1,000 hours? 7.2 more than 950 hours? 7.3 less than 790 hours? 7.4 less than 805 hours?

CED 6030 HOMEWORK 2 NU ID# Name You must show your problem solving process. A solution only cannot get any credits. 1. Given the probabilities in the table below for events in a sample space S, find the following probabilities. A B C D Totals E 0.02 0.08 0.06 0.04 0.2 F 0.05 0.1 0.3 0.35 0.8 Totals 0.07 0.18 0.36 0.39 1.00 1.1 P(B) 1.2 P(A n F) 1.3 P(D | E) 1.4 P(C | C)CED 6030 Winter 2021 4. The following table gives the probability distribution of the number of flights that are overbooked per day for Boston Airlines. Number of Flights Overbooked 0 2 3 4 Probability 0.2 0.2 0.4 0.1 0.1 4.1 Find the expected number of flights that are overbooked per day. 4.2 What is the standard deviation in the number of flights that are overbooked per day?CED 6030 Winter 2021 3. Find the probabilities by referring to the following tree diagram and using Bayes' formula. 0.3 0.2 A 0.5 0.3 0.2 D 0.5 0.7 Start m 0.1 0.2 0.4 0.4 E 0.2 F 3.1 P(B | F) 3.2 P(A | E) 3.3 P(C | D)CED 603i} Winter 2021 2. Refer to the following experiment: 2 balls are drawn in succession out of a box containing 2 red and 5 white balls. Let R; be the event that the i th ball ls red, and let W1 he the event that the i th bell is white. Construct a [:Irobabilitg,r tree for this experiment and nd the probability of each of the events H: P! 32,131 Fl W2, W; 0 R2. W; I"| W2, given that the rst hall drawn was 2.1 Replaced before the second draw 2.2 Not replaced before the second draw CED 603i} Winter 2021 2. Refer to the following experiment: 2 balls are drawn in succession out of a box containing 2 red and 5 white balls. Let R; be the event that the i th ball ls red, and let W1 he the event that the i th bell is white. Construct a [:Irobabilitg,r tree for this experiment and nd the probability of each of the events H: P! 32,131 Fl W2, W; 0 R2. W; I"| W2, given that the rst hall drawn was 2.1 Replaced before the second draw 2.2 Not replaced before the second draw CED 6030 Winter 2021 5. Use the following data for this question. Car Miles per gallon (MPG) 2017 AUDI A4 37 2017 AUDI A3 35 2017 AUDI A6 34 2017 BMW 3201 35 2017 BMW 5301 33 2017 BMW 3301 34 2017 LEXUS ES300 39 2017 LEXUS CT200 40 2017 LEXUS GS450 34 2017 VOLVO S60 36 2017 VOLVO $90 34 Find the mean, median, and mode for the data.CED 6030 HOMEWORK 2 NU ID# Name You must Show your problem solving process. A solution only cannot get any credits. 1. Given the probabilities in the table below for events in a sample space S, nd the following probabilities. Totals 007 0.18 0.36 0.39 1.00 1.1P(B) 1.2 P(A n F) 1.3 P(D |E) CED 6030 HOMEWORK 2 NU ID# Name You must Show your problem solving process. A solution only cannot get any credits. 1. Given the probabilities in the table below for events in a sample space S, nd the following probabilities. Totals 007 0.18 0.36 0.39 1.00 1.1P(B) 1.2 P(A n F) 1.3 P(D |E)