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On average 38 % of Finite Mathematics students don't spend any time in the Mathematics Department's resource room (event R₁), 31% of the students spend between 1 and 90 minutes in the resource room (event R₂) and 31 % of the students more than 90 minutes per week in the resource room (event R3). At the end of the semester the students in the class were asked how many minutes per week they spent in the resource room and whether they passed or failed. The passing rates are summarized in the following table: Time spent in resource room Pass % None 23 Between 1 and 90 minutes 48 69 More than 90 minutes If a randomly chosen student did pass the course, what is the probability that: a) He or she did not study in the resource room? P(did not study | pass) = b) He or she studied between 1 and 90 minutes in the resource room? P(studied 1 to 90 | pass) = c) He or she studied more than 90 minutes in the resource room? P(studied> 90 | pass) =: Hint: If we denote by Q the event that a student passes the course the above table gives P(QR.) for i= 1. 2. 3 and P(R.) are given in the text. You are asked for P(RO)

On average 38 % of Finite Mathematics students don't spend any time in the Mathematics Department's resource room (event R₁), 31% of the students spend between 1 and 90 minutes in the resource room (event R₂) and 31 % of the students more than 90 minutes per week in the resource room (event R3). At the end of the semester the students in the class were asked how many minutes per week they spent in the resource room and whether they passed or failed. The passing rates are summarized in the following table: Time spent in resource room Pass % None 23 Between 1 and 90 minutes 48 69 More than 90 minutes If a randomly chosen student did pass the course, what is the probability that: a) He or she did not study in the resource room? P(did not study | pass) = b) He or she studied between 1 and 90 minutes in the resource room? P(studied 1 to 90 | pass) = c) He or she studied more than 90 minutes in the resource room? P(studied> 90 | pass) =: Hint: If we denote by Q the event that a student passes the course the above table gives P(QR.) for i= 1. 2. 3 and P(R.) are given in the text. You are asked for P(RO)

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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On average 38 % of Finite Mathematics students don't spend any time in the Mathematics Department's resource room (event R₁), 31 % of the students spend between 1 and 90 minutes in the resource room (event R₂) and 31 % of the students more than 90 minutes per week in the resource room (event R3). At the end of the semester the students in the class were asked how many minutes per week they spent in the resource room and whether they passed or failed. The passing rates are summarized in the following table: Time spent in resource room Pass None 23 Between 1 and 90 minutes 48 69 More than 90 minutes If a randomly chosen student did pass the course, what is the probability that: a) He or she did not study in the resource room? P(did not study | pass) = b) He or she studied between 1 and 90 minutes in the resource room? P(studied 1 to 90 | pass) = c) He or she studied more than 90 minutes in the resource room? P(studied > 90 | pass) =: Hint: If we denote by the event that a student passes the course above table gives P(Q|R₂) for i = 1, 2, 3 and P(R₂) are given in the text. You are asked for P(R₂|Q)
Transcribed Image Text:On average 38 % of Finite Mathematics students don't spend any time in the Mathematics Department's resource room (event R₁), 31 % of the students spend between 1 and 90 minutes in the resource room (event R₂) and 31 % of the students more than 90 minutes per week in the resource room (event R3). At the end of the semester the students in the class were asked how many minutes per week they spent in the resource room and whether they passed or failed. The passing rates are summarized in the following table: Time spent in resource room Pass None 23 Between 1 and 90 minutes 48 69 More than 90 minutes If a randomly chosen student did pass the course, what is the probability that: a) He or she did not study in the resource room? P(did not study | pass) = b) He or she studied between 1 and 90 minutes in the resource room? P(studied 1 to 90 | pass) = c) He or she studied more than 90 minutes in the resource room? P(studied > 90 | pass) =: Hint: If we denote by the event that a student passes the course above table gives P(Q|R₂) for i = 1, 2, 3 and P(R₂) are given in the text. You are asked for P(R₂|Q)
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