Purchase Solution

Simple Probability - Bayes Theorem and Venn Diagrams

Not what you're looking for?

Ask Custom Question

1. In each one of the following cases, indicate classic probability is used, empirical (relative occurrence frequency) or subjective.
a. A basketball player fails 30 of 50 distances. The probability that he fails the following shot is .60.
b. A committee of seven students forms to study the environmental questions. What is the possibility that one of them is chosen like spokesman?
c. You buy one of the 4 million tickets of Lottery. What is the probability that you win the prize of 1 million?
d. The probability of a tremor in the north of California in next the 10 years is of 80, according to Mr. Ritcher Osmond, specialist in seismology.

2. Out of 200 students in the business administration department, 50 are registered for Basic Accounting, 60 are registered for Economics and other 40 are taking both courses.
a. Draw the Venn diagram.
b. Determine the probability that a chosen student at random is in both courses.

3. A professor has 30 students in two groups of accounting, Group A and Group B. The group A has 20 students, of which 5 will take the test for CPA. From group B, 4 will take the test for CPA. The other students will not take the test.
a. Draw a probability tree representing the described situation.
b. Determine the probability that a chosen student at random is going to take the test for CPA.

4. Suppose that two events A and B are mutually exclusive. Determine the probability that they happen jointly.

5. The manager of Puerto Rican Airlines is worried about the possibility of strikes in the company. He knows that the probability that their pilots go on strike is 0.75 and the probability that the drivers go on strike is 0.65. In addition, he knows that if the conductors go on strike, the pilots have a probability of .90 also of going on strike.
a. Determine the probability that both groups go on strike.
b. Determine the probability that the conductors go on strike if the pilots go on strike.

6. The probability that a publicity campaign increases sales is .80. The probability that the cost of developing that campaign stays within the budget is .40. Suppose that the events are independent, determine the probability that the cost stays within budget.

Attachments
Purchase this Solution
Solution Summary

Problem 5
a) Using Bayes' Theorem, we know that the probability of both groups striking is equal to P(pilots strike | conductors strike) * P(conductors strike) = 0.9 * 0.65 = 0.585
b) Using Bayes' Theorem again, we know that P(conductors strike | pilots strike) = P(conductors strike AND pilots strike)/P(pilots strike) = 0.585/0.75 = 0.78

Solution Preview

Problem 1
Classical probability is based on calculation of the likelihood without observation. Empirical probability is derived based on previous observation. Subjective probability is derived based on non-quantitative knowledge, such as a gut feeling.

Thus a) is empirical, b) is classical, since you can calculate that one out of seven will be chosen, c) is classical, and d) is subjective.

Problem 2
A Venn diagram summarizes the number of students registered in each course and in both courses. See the link below for more details on Venn diagrams:
http://en.wikipedia.org/wiki/Venn_diagram

See the Venn ...

Purchase this Solution
Free BrainMass Quizzes
Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

View More Free Quizzes
Related BrainMass Solutions

  • Use of Bayes' theorem in health care administration

    An Intuitive (and Short) Explanation of Bayes' Theorem.

  • Applied Statistics in Business

    In a contingency table, explain the concepts of (a) marginal probability and (b) joint probability. 9. Why are tree diagrams useful? Why are they not always practical? 10. What is the main point of Bayes's Theorem? 11.

  • Bayes's theorem

    172602 Bayes's Theorem Explain Bayes's theorem, and give a practical example of how it can be used. Be specific. Bayes' theorem (also known as Bayes' rule or Bayes' law) is a result in probability theory that relates conditional probabilities.

  • Bayes' Theorem for Probability Revision

    144567 Bayes' Theorem for Probability Revision Set up a short problem related to your work environment to calculate the probability(ies) of an event happening. Then use Bayes' Theorem to revise the probability. Show all your work.

  • Venn Diagrams and Probability

    179473 Venn Diagrams and Probability Solve using venn diagrams a and b are events in a sample space S such that P(A)=0.7,P(B)0.4 and P(A and B) = 0.2.

  • Describing a Bayes Theorem Application

    167814 Describing a Bayes Theorem Application Bayes theorem is very important, since it forms the basis of much of our thinking in conditional probability and making "predictions" statistically based on historical data.

  • Probability - Bayes' Theorem

    58142 Probability - Bayes' Theorem The Question is: An estimated 8% of men and O.5% of women are colorblind. If a colorblind person is selected at random, what is the probability that the person is a man?

  • Probability : Bayes' Theorem

    36914 Probability : Bayes' Theorem In a survey, it is found that 10 boys out of hundred are in favor of selecting their life partners themselves without any interference by their parents. Where as only 20 girls out of 500 hold this view.

  • Prostate Cancer Test

    Suppose there is a .02 probability that a male patient has prostate cancer before testing. The probability of a false-positive test is .75, and the probability of a false-negative (no indication of cancer when cancer is actually present) is .20.

View More Related Solutions