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Lecture 11 & 12: 1. An urn contains 6 red, 7 blue, and 5 green balls. You draw out two balls and they are different colors. Given this, what is the probability that the two balls were red and blue? 2. The following is a table showing the number of regular and irregular students in CSE230 live consultation hours and their grades in the viva voce. Good Average Bad Total Regular 22 5z-5 Irregular W z+3 V u Total 23 u+2 u-v 40 What is the probability that a student gets a bad grade in viva given that s/he is irregular in consultation? [Hint: You need to determine the unknowns first] 3. An almost out-of-business movie theatre has three categories of seats - front, middle, and rear. Of the total number of seats, 10% are front seats, 30% are middle seats, and the rest are rear seats. It is known from previous experience of movie-goers that 5% of the front seats, 10% of middle seats, and 20% of the rear seats are broken. Determine the probability of a randomly selected seat being broken.

Lecture 11 & 12: 1. An urn contains 6 red, 7 blue, and 5 green balls. You draw out two balls and they are different colors. Given this, what is the probability that the two balls were red and blue? 2. The following is a table showing the number of regular and irregular students in CSE230 live consultation hours and their grades in the viva voce. Good Average Bad Total Regular 22 5z-5 Irregular W z+3 V u Total 23 u+2 u-v 40 What is the probability that a student gets a bad grade in viva given that s/he is irregular in consultation? [Hint: You need to determine the unknowns first] 3. An almost out-of-business movie theatre has three categories of seats - front, middle, and rear. Of the total number of seats, 10% are front seats, 30% are middle seats, and the rest are rear seats. It is known from previous experience of movie-goers that 5% of the front seats, 10% of middle seats, and 20% of the rear seats are broken. Determine the probability of a randomly selected seat being broken.

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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Lecture 11 & 12: 1. An urn contains 6 red, 7 blue, and 5 green balls. You draw out two balls and they are different colors. Given this, what is the probability that the two balls were red and blue? 2. The following is a table showing the number of regular and irregular students in CSE230 live consultation hours and their grades in the viva voce. Good Average Bad Total Regular 22 2 5z-5 Irregular V u W z+3 Total 23 u+2 u-v 40 What is the probability that a student gets a bad grade in viva given that s/he is irregular in consultation? [Hint: You need to determine the unknowns first] 3. An almost out-of-business movie theatre has three categories of seats - front, middle, and rear. Of the total number of seats, 10% are front seats, 30% are middle seats, and the rest are rear seats. It is known from previous experience of movie-goers that 5% of the front seats, 10% of middle seats, and 20% of the rear seats are broken. Determine the probability of a randomly selected seat being broken.
Transcribed Image Text:Lecture 11 & 12: 1. An urn contains 6 red, 7 blue, and 5 green balls. You draw out two balls and they are different colors. Given this, what is the probability that the two balls were red and blue? 2. The following is a table showing the number of regular and irregular students in CSE230 live consultation hours and their grades in the viva voce. Good Average Bad Total Regular 22 2 5z-5 Irregular V u W z+3 Total 23 u+2 u-v 40 What is the probability that a student gets a bad grade in viva given that s/he is irregular in consultation? [Hint: You need to determine the unknowns first] 3. An almost out-of-business movie theatre has three categories of seats - front, middle, and rear. Of the total number of seats, 10% are front seats, 30% are middle seats, and the rest are rear seats. It is known from previous experience of movie-goers that 5% of the front seats, 10% of middle seats, and 20% of the rear seats are broken. Determine the probability of a randomly selected seat being broken.
4. An insurance company classifies people into one of the three classes – good risks, average risks and bad risks. 30% of the population are labelled as "good risk", 60% as "average risk" and the remaining as "bad risk". Their records indicate that over a 1-year span 10% of good risk people, 20% of average risk people, and 30% of bad risk people are involved in an accident.Determine the probability of a randomly selected policy holder being involved in an accident. 5. Bag A contains 6 red and 7 black balls and Bag B contains 9 red and 6 black balls. One ball is transferred from Bag A to Bag B and then a ball is drawn from Bag B. The ball so drawn is found to be black in color. Find the probability that the transferred ball was red. 6. Suppose there are 8 fair coins and 12 unfair coins in a bag such that the unfair coins have a 75% probability of landing heads. A coin is randomly picked from the bag and flipped 9 times. If the coin landed heads 7 times out of 9, what is the probability that the coin to be unfair? 7. Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drugs reduces its chances by 25%. At a time, a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?
Transcribed Image Text:4. An insurance company classifies people into one of the three classes – good risks, average risks and bad risks. 30% of the population are labelled as "good risk", 60% as "average risk" and the remaining as "bad risk". Their records indicate that over a 1-year span 10% of good risk people, 20% of average risk people, and 30% of bad risk people are involved in an accident.Determine the probability of a randomly selected policy holder being involved in an accident. 5. Bag A contains 6 red and 7 black balls and Bag B contains 9 red and 6 black balls. One ball is transferred from Bag A to Bag B and then a ball is drawn from Bag B. The ball so drawn is found to be black in color. Find the probability that the transferred ball was red. 6. Suppose there are 8 fair coins and 12 unfair coins in a bag such that the unfair coins have a 75% probability of landing heads. A coin is randomly picked from the bag and flipped 9 times. If the coin landed heads 7 times out of 9, what is the probability that the coin to be unfair? 7. Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduces the risk of heart attack by 30% and prescription of certain drugs reduces its chances by 25%. At a time, a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?
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