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

Undergraduate Major

Business

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