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B 1 A 0.14 0.02 0.09 1 0.05 0.29 0.05 2 0.10 0.13 0.13 a. What is the probability that there is at most one self -service and at most one full-service hose during this event? b. Give a word description of the event {A#1 and B#1}, compute the probability of this event. c. What is the probability that there is exactly one hose used in self-service during an event? d. Compute the marginal pmf of A and of B. Using PA(A), what is P(A<=1)? Are A and B independent events? Explain. 2.

B 1 A 0.14 0.02 0.09 1 0.05 0.29 0.05 2 0.10 0.13 0.13 a. What is the probability that there is at most one self -service and at most one full-service hose during this event? b. Give a word description of the event {A#1 and B#1}, compute the probability of this event. c. What is the probability that there is exactly one hose used in self-service during an event? d. Compute the marginal pmf of A and of B. Using PA(A), what is P(A<=1)? Are A and B independent events? Explain. 2.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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12:58 ul 4G Step2 b) a)The probability that there was at most one self service and one full service is, P(A < 1, B< 1)=P(0, 0)+P(0, 1)+P(1, 0)+P( =0. 14 + 0. 02+ 0. 29 + 0. 05 =0. 5 Hence, the required probability is 0.5. b) {A + 1 and B+ 1} shows that hoses required for self service and full service are not equal to 1. The probability of P(A+ 1NB + 1) is, P(A + 1NB ± 1)=P(0, 0)+P(0, 2)+P(2, 0)+P( =0. 14 + 0.1+ 0. 09 + 0. 13 =0. 46 Step3 c) c)The probability that there was exactly one self service and one full service is, P(A = 1, B= 1)=P(1, 1) =0. 05 Hence, the required probability is 0.05.
Transcribed Image Text:12:58 ul 4G Step2 b) a)The probability that there was at most one self service and one full service is, P(A < 1, B< 1)=P(0, 0)+P(0, 1)+P(1, 0)+P( =0. 14 + 0. 02+ 0. 29 + 0. 05 =0. 5 Hence, the required probability is 0.5. b) {A + 1 and B+ 1} shows that hoses required for self service and full service are not equal to 1. The probability of P(A+ 1NB + 1) is, P(A + 1NB ± 1)=P(0, 0)+P(0, 2)+P(2, 0)+P( =0. 14 + 0.1+ 0. 09 + 0. 13 =0. 46 Step3 c) c)The probability that there was exactly one self service and one full service is, P(A = 1, B= 1)=P(1, 1) =0. 05 Hence, the required probability is 0.05.
Problem 3 In Muscat city, there are two types of services at a gas station. The gas station has a single regular lead-free pump with two hoses. In this context, A indicates the number of hoses being utilized on the self-service station at a certain time and B indicates the number of hoses on the full-service station utilizes at that time. The joint pmf of A and B i.e., fazAB) is shown below. В 1 2 A 0.14 0.02 0.05 0.29 0.10 0.13 0.09 1 0.05 0.13 a. What is the probability that there is at most one self -service and at most one full-service hose during this event? b. Give a word description of the event {A#1 and B#1}, compute the probability of this event. c. What is the probability that there is exactly one hose used in self-service during an event? d. Compute the marginal pmf of A and of B. Using PA(A), what is P(A<=1)? Are A and B independent events? Explain.
Transcribed Image Text:Problem 3 In Muscat city, there are two types of services at a gas station. The gas station has a single regular lead-free pump with two hoses. In this context, A indicates the number of hoses being utilized on the self-service station at a certain time and B indicates the number of hoses on the full-service station utilizes at that time. The joint pmf of A and B i.e., fazAB) is shown below. В 1 2 A 0.14 0.02 0.05 0.29 0.10 0.13 0.09 1 0.05 0.13 a. What is the probability that there is at most one self -service and at most one full-service hose during this event? b. Give a word description of the event {A#1 and B#1}, compute the probability of this event. c. What is the probability that there is exactly one hose used in self-service during an event? d. Compute the marginal pmf of A and of B. Using PA(A), what is P(A<=1)? Are A and B independent events? Explain.
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