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?
This is review. Not graded. Please help. Old review question.
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).
Expert Solution
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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. Andintersection of A and B, is the occurrence of A and B both.
The probability of occurrence of A or B is given by,
![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).](https://content.bartleby.com/qna-images/question/e8f98c03-2dea-45fe-9e7d-c001811b98bd/bd3a9bbc-0b43-4925-8231-3bbaae81a140/7xs4iqc_processed.jpeg)
