Ap Statistics Solutions To Packet 6 - Probability The Study Of Randomness Worksheet With Answers Page 18
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216.67 ACADEMIC DEGREES Here are the counts (in thousands) of earned degrees in the United
States in a recent year, classified by level and by the sex of the degree recipient:
Bachelor’s
Master’s
Professional
Doctorate
Total
Female
616
194
30
16
856
Male
529
171
44
26
770
Total
1145
365
74
42
1626
(a) If you choose a degree recipient at random, what is the probability that the person you choose is a
856
=
woman?
0.5264
1626
(b) What is the conditional probability that you choose a woman, given that the person chosen
30
=
received a professional degree?
0.4054
74
(c) Are the events “choose a woman” and “choose a professional degree recipient” independent?
How do you know?
No: If they were independent, the answers to (a) and (b) would be the same.
6.70 TEENAGE DRIVERS An insurance company has the following information about drivers
aged 16 to 18 years: 20% are involved in accidents each year; 10% in this age group are A students;
among those involved in an accident, 5% are A students.
(a) Let A be the event that a young driver is an A student and C the event that a young driver is
involved in an accident this year. State the information given above in terms of probabilities and
conditional probabilities for the events A and C.
P(C) = 0.20, P(A) = 0.10, P(A | C) = 0.05.
(b) What is the probability that a randomly chosen young driver is an A student and is involved in an
P(A and C) = P(C) × P(A | C) = (0.20)(0.05) = 0.01.
accident?
18
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