# Probability Problems

Probability Problems
For problems 1-10 consider the experiment where two dice are thrown simultaneously. If both die do not have a clear upward facing side, the dice are thrown again. Each dice has six faces, numbered 1-6. Assume that the dice are fair and that each side is equally likely to occur and the dice do not influence each other.
1. What is the probability that the sum of the upward facing sides of both dice is equal to two
2. What is the probability the sum of the upward facing sides of both dice is equal to three
3. What is the probability the sum of the upward facing sides of both dice is equal to seven
4. What is the probability the upward facing sides of the two die are the same
5. What is the probability the upward facing sides of the two die are different
6. What is the probability that at least one of the upward facing sides of the dice is a four, five or six
7. What is the probability that exactly one of the upward facing sides of the dice is a four, five or six
8. What is the probability that none of the upward facing sides of the dice is a four, five or six
9. After throwing the two die, you observe that one of them is a six. What is the probability that the second dice is also a six
10. After throwing the two die, you observe that one of them is a six. What is the probability that the second dice is not a six
Given the following probabilities, answer questions 11-25. Remember that A is called the complement of A, and P(A) = 1- P(A).

A
A
Totals
B
0.18
0.45
0.63

0.24
0.13
0.37
Totals
0.42
0.58
1.00
11. What is the P(A)
12. What is the P(B)
13. What is the P(A)
14. What is the P(A and B)
15. What is the P(A and )
16. What is the P(A and A)
17. What is the P(A|B)
18. What is the P(A|B)
19. What is the P(B|A)
20. What is P(A| A)
21. What is the P(A or B)
22. What is the P(A or A)
23. What is the P(A and A)
24. Are A and A independent of each other
25. Are A and B independent of each other
For problems 26-30, suppose P(A) = 0.54 and P(B|A) = 0.27 and P(B| A) = 0.68
26. What is P(A)
27. What is P(A| B)
28. What is P(A|)
29. What is P(B) =
30. Is A independent of B
For problems 31-35, suppose P(A) = 0.42 and P(B|A) = 0.34 and P(B| A) = 0.34 .
31. What is P(A)
32. What is P(A| B)
33. What is P(A|)
34. What is P(B)
35. Is A independent of B
Note: For the following two Bonus Questions, please manually add any extra credit points to the student’s grade.
36. (Bonus Question) Suppose X is the amount of money a person earns in an hour where
P(X = \$5) .2, P(X =\$10) = 0.1, P(X=\$15) .5 and P(X=\$20) = 0.2.
How much money would the person earn on average
37. (Bonus Question) If the payoff of rolling two dice is the sum of the upper face of the two dice, what is the expected payoff of one roll of the two dice

# Our Service Charter

1. ### Excellent Quality / 100% Plagiarism-Free

We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarism-free. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers.
2. ### Free Revisions

We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed.
3. ### Confidentiality / 100% No Disclosure

We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service.
4. ### Money Back Guarantee

If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 14-30 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% money-back in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit.

We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.

Excellent Quality
Zero Plagiarism
Expert Writers

or

Instant Quote