AP Statistics, Semester 1 Page 1 of 3 Assignment: Using the Rules of Probability

1. You roll a pair of standard dice. Create the sample space for a single roll of the dice and use the sample space to compute the following probabilities. (5 points total. 1 pt. for each part of the question.)

A. Create a sample space.

B. P (getting a 1 on the first die or getting a 5 on the second die)

C. P (sum of the dice = 10)

D. P (getting a 3 on the second die given that you got a 2 on the first die)

E. P (getting an odd number on the first die and a value greater than 4 on the

second die)

2. Below is some hypothetical data on the voting preferences of individuals of different religious affiliations.

Vote in 1996

Election Religion A Religion B Religion C TOTAL

Green Party 280 350 300 930 Blue Party 245 435 230 910 Orange Party 100 80 85 265 TOTAL 625 865 615 2,105

Use this information to compute the following probabilities: (4 points total. 1 pt. for each part of the question.)

A. P (Vote for Orange Party) B. P (Vote for Green Party or Religion C) C. P (Vote for Blue Party, given that individual is Religion C) D. P (Religion B, given that individual voted for Orange Party) 3. The hypothetical probabilities of types of weather in two neighborhoods in San Francisco

on an average day in the month of August are shown below: Sunset neighborhood

35% chance of sunshine 50% chance of fog cover 15% chance of rain

Mission Neighborhood

70% chance of sunshine 10% chance of fog cover 20% chance of rain

AP Statistics, Semester 1 Page 2 of 3 Assignment: Using the Rules of Probability

Compute the following probabilities: (4 points total. 1 point for each part of the question.)

A. P (fog in the Sunset and sunshine in the Mission) B. P (sunny in the Sunset for three consecutive days) C. P (fog in the Sunset or fog in the Mission) D. P (rain in the Mission given that it is not sunny in the Mission)

4. In a random sample of male and female graduates of the New York School for the Arts between the ages of 22-35 you know that:

• the probability a man is a ballet dancer is 0.245.

• the probability a woman is a musical performer is 0.365

• the probability a man is a musical performer, given that he's a ballet dancer is 0.250.

• the probability a woman is an actress is 0.550.

• the probability a woman is an actress, given that she's a musical performer is .785.

Compute the following probabilities: (3 points total. 1 point for each part of the question.)

A. P (man is a ballet dancer and a musical performer) B. P (woman is an actress and a musical performer) C. P (woman is an actress or a musical performer)

5. A college student frequents one of two coffee houses on campus, choosing Starbucks 70% of the time and Peetes 30% of the time. Regardless of where she goes, she buys a café mocha on 60% of her visits. (5 points total. 1 point for part B. 1-1/3 points for each parts A, C, and D.)

A. Probability of going to Starbucks and ordering a café mocha is: B. Are the two events in part A independent?

C. Probability of (Peete's | ordered a mocha)

D. Probability of Starbucks OR orders Café Mocha

AP Statistics, Semester 1 Page 3 of 3 Assignment: Using the Rules of Probability

6. Whether a grant proposal is funded quite often depends on the reviewers. Suppose a group of research proposals was evaluated by a group of experts as to whether the proposals were worthy of funding. When these same proposals were submitted to a second independent group or experts, the decision to fund was reversed in 30% of the cases. If the probability that a proposal is judged worthy of funding by the first peer review group is .2, what are the probabilities of these events? (4 points. 1-1/3 point for each part of the question.)

A. Worthy Proposal is approved by both groups

B. Worthy proposal disapproved by both groups

C. Worthy proposal is approved by one group

Acknowledgements Question 5: This is question 4.58 (a, b, c, d) from page 150 of Introduction to Probability and Statistics, Tenth Edition, by W. Mendenhall, R. Beaver, and B. Beaver. Copyright © 1999 by Brooks Cole, division of Thompson Learning Incorporated. Further reproduction is prohibited without permission of the publisher. Question 6: This is question 4.53 (a, b, c,) from page 149 of Introduction to Probability and Statistics, Tenth Edition, by W. Mendenhall, R. Beaver, and B. Beaver. Copyright © 1999 by Brooks Cole, division of Thompson Learning Incorporated. Further reproduction is prohibited without permission of the publisher. ____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc.