# Worksheet 5: Probability II

Worksheet 5 (Chapter 3): Probability II
Name: ______________________________________________

Section: _________________________

For any of the following questions be sure to show appropriate work and give appropriate probability statements.
1. Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows.

Intended
Enrollment
Status

Full-Time
Part-Time
Totals

Engineering
352
197
150
161
502
358

Other
251
194
445

Totals
800
505
1305

a. If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate engineering major?
P(Engineering | full-time) = 197/800 = 0.2463

b. If a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree?

P(full time | business) = 352/502 = 0.7012

c. Let A denote the event that the student intends to attend classes full-time in pursuit of an MBA degree, and let B denote the event that the student was an undergraduate business major. Are events A and B independent? Justify your answer.

Can use either method
P(A) = 800/1305 = 0.6130
P(A) = 800/1305 = 0.6130
P(A|B) = 352/502 = 0.7012
P(B) = 502/1305 = 0.3847
P(A and B) = 352/1305 = 0.2697
P(A) ≠ P(A|B) therefore A and B are not
P(A)P(B) = 0.6130 x 0.3847 = 0.2358
independent
P(A)P(B) ≠ P(A and B) therefore A and B are
Also works for P(B) ≠ P(B|A)
not indepedent

2. Jamal Crawford of the National Basketball Association’s Portland Trail Blazers is the best free-throw shooter on the team, making 93% of his shots (ESPN website, April 5, 2012). Assume shots are independent and that late in a basketball game, Jamal Crawford is fouled and is awarded two shots. a. What is the probability that...