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?

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