# Worksheet 5: Probability II

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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
What is the probability that he will make at least one shot?
Sample Space (makes both, makes first misses second, misses first makes second, misses both)
P(makes at least one out of two) = 1 – P(misses both) = 1 – (0.07)(0.07) = 0.9951
c. What is the probability that he will miss both shots?
P(misses both) = (0.07)(0.07) = 0.0049

3. Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic (debit and credit) cards in making purchases (Associated Press, January 16, 2006). The results of the study of consumers older than 18 provided the following probabilities.
• The probability that a consumer uses a plastic card when making a purchase is 0.37.
• Given that the consumer uses a plastic card, there is a 0.19 probability that the consumer is 18 to
24 years old.
• Given that the consumer uses a plastic card, there is a 0.81 probability that the consumer is more than 24 years old.
US Census Bureau data show that 14% of the consumer population is 18 to 24 years old.
a. Given the consumer is 18 to 24 years old, what is the probability that the consumer uses a plastic card? Uses plastic
Does not use plastic

18 – 24
(0.37)(.19) = 0.0703
0.14 – 0.0703 = 0.0697
0.14

Older than 24
(0.37)(0.81) = 0.2997
0.86 – 0.2997 = 0.5603
1.00 – 0.14 = 0.86

Total
0.37
1.00 – 0.37 = 0.63
1.00

P(plastic | 18 to 24) = 0.0703/0.14 = 0.5021
b. Given the consumer is over 24 years old, what is the probability that the