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1. Tom and Jerry are brothers in a math class. The teacher estimates that for each class, the probabilities that Tom and Jerry come late are 10% and 16% respectively. And the probability that they are both late is 5%. Assume the teacher's estimation is correct, find the following probabilities. (a) [12 points] In a particular class, what is the probability that both Tom and Jerry are present on time? (b) [12 points] In a particular class, if it's known that Tom is late, what is the probability that Jerry is also late?

1. Tom and Jerry are brothers in a math class. The teacher estimates that for each class, the probabilities that Tom and Jerry come late are 10% and 16% respectively. And the probability that they are both late is 5%. Assume the teacher's estimation is correct, find the following probabilities. (a) [12 points] In a particular class, what is the probability that both Tom and Jerry are present on time? (b) [12 points] In a particular class, if it's known that Tom is late, what is the probability that Jerry is also late?

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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1. Tom and Jerry are brothers in a math class. The teacher estimates that for each class, the probabilities that Tom and Jerry come late are 10% and 16% respectively. And the probability that they are both late is 5%. Assume the teacher's estimation is correct, find the following probabilities. (a) [12 points] In a particular class, what is the probability that both Tom and Jerry are present on time? (b) [12 points] In a particular class, if it's known that Tom is late, what is the probability that Jerry is also late? 2. Consider an experiment of rolling five dice. (a) [12 points] What is the probability that the five dice come up different values? (b) [14 points] What is the probability of obtaining two odd numbers and three even numbers? 3. In a bag, there are 8 blue marbles, 10 red marbles and 12 green marbles. When 4 marbles are randomly chosen from the bag, find each of the following probabilities. (a) [12 points] What is the probability that all chosen marbles have the same color? (b) [14 points] If it's known that none of the chosen marbles are green, what is the probability of getting more blue marbles than red marbles? 4. Let A and B be events. (a) [12 points] Assume P(A) = 0.57, P (B) = 0.78, and P(A n B) = 0.42. Find P(A U BC). (b) [12 points] Assume P(A) = 0.57, P(B) = 0.78, and P(A | B) = 0.65. Find P (B|A).
Transcribed Image Text:1. Tom and Jerry are brothers in a math class. The teacher estimates that for each class, the probabilities that Tom and Jerry come late are 10% and 16% respectively. And the probability that they are both late is 5%. Assume the teacher's estimation is correct, find the following probabilities. (a) [12 points] In a particular class, what is the probability that both Tom and Jerry are present on time? (b) [12 points] In a particular class, if it's known that Tom is late, what is the probability that Jerry is also late? 2. Consider an experiment of rolling five dice. (a) [12 points] What is the probability that the five dice come up different values? (b) [14 points] What is the probability of obtaining two odd numbers and three even numbers? 3. In a bag, there are 8 blue marbles, 10 red marbles and 12 green marbles. When 4 marbles are randomly chosen from the bag, find each of the following probabilities. (a) [12 points] What is the probability that all chosen marbles have the same color? (b) [14 points] If it's known that none of the chosen marbles are green, what is the probability of getting more blue marbles than red marbles? 4. Let A and B be events. (a) [12 points] Assume P(A) = 0.57, P (B) = 0.78, and P(A n B) = 0.42. Find P(A U BC). (b) [12 points] Assume P(A) = 0.57, P(B) = 0.78, and P(A | B) = 0.65. Find P (B|A).
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"Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question."

 

For any two events A and B, union of A and B, is the occurrence of either A or B or both. And intersection of A and B, is the occurrence of A and B both.

The probability of occurrence of A or B is given by,

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