AP Statistics with 6 Practice Tests

Martin Sternstein

Chapter 4

Probability, Random Variables, and Probability Distributions - all with Video Answers

Educators

Section 14

Quiz 14

Problem 1

One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.
What is the probability that a student has a GPA between 2.0 and $3.0 ?$
(A) $\frac{5}{9} \times$
(B) $\frac{5}{9} \times$
(C) $\frac{25}{1,000}$
(D) $\frac{450}{1,000}$
(E) $\frac{450}{1,000}$
(E) $\frac{450}{1,000}$

Tyler Moulton

Tyler Moulton

Numerade Educator

Problem 2

One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.
What is the probability that a student has a GPA under 2.0 and has skipped many classes?
(A) $\frac{5}{9} \times$
(B) $\frac{5}{9} \times$
(C) $\frac{25}{1,000}$
(D) $\frac{110+255}{1,000}$
(E) $\frac{110+255-80}{1,000}$

Tyler Moulton

Numerade Educator

Problem 3

One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.
What is the probability that a student has a GPA under 2.0 or has skipped many classes?
(A) $\frac{5}{9} \times$
(B) $\frac{5}{9} \times$
(C) $\frac{25}{1,000}$
(D) $\frac{110+255}{1,000}$
(E) $\frac{110+255-80}{1,000}$

Tyler Moulton

Numerade Educator

Problem 4

One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.
What is the probability that a student has a GPA under 2.0 given that he has skipped many classes?
(A) $\frac{5}{9} \times$
(B) $\frac{5}{9} \times$
(C) $\frac{5}{9} \times$
(D) $\frac{25}{1,000}$
(E) $\frac{25}{1,000}$

Tyler Moulton

Numerade Educator

Problem 5

One thousand students at a city high school were classified both according to GPA and whether or not they consistently skipped classes.
Are "GPA between 2.0 and 3.0 " and "skipped few classes" independent?
(A) No, because $0.475 \neq 0.506$.
(B) No, because $0.475 \neq 0.890$.
(C) No, because $0.450 \neq 0.475$.
(D) Yes, because of conditional probabilities.
(E) Yes, because of the product rule.

Tyler Moulton

Numerade Educator

Problem 6

The following data are from The Commissioner's Standard Ordinary Table of Mortality:
\What is the probability that a 20-year-old will survive to be
$70 ?$
(A) $\frac{5,592,012}{9,664,994}$
(B) $\frac{5,592,012}{10,000,000}$
(C) $\frac{5,592,012}{10,000,000}$
(D) $1-\frac{5,592,012}{9,664,994}$
(E) $\frac{1-\frac{5,592,012}{9,664,994}}{10,000,000}$

Tyler Moulton

Numerade Educator

Problem 7

In a 1974 "Dear Abby" letter, a woman lamented that she had just given birth to her eighth child and all were girls! Her doctor had assured her that the chance of the eighth child being a girl was less than 1 in 100 . What was the real probability that the eighth child would be a girl?
(A) 0.0039
(B) 0.5
(C) $(0.5)^{7}$
(D) $(0.5)^{8}$
(E) $\frac{(0.5)^{7}+(0.5)^{8}}{2}$

Tyler Moulton

Numerade Educator

Problem 8

There are two games involving flipping a fair coin. In the first game, you win a prize if you can throw between $40 \%$ and $60 \%$ heads. In the second game, you win if you can throw more than $75 \%$ heads. For each game, would you rather flip the coin 50 times or 500 times?
(A) 50 times for each game
(B) 5 oo times for each game
(C) 50 times for the first game, and 5 oo for the second
(D) 5 oo times for the first game, and 50 for the second
(E) The outcomes of the games do not depend on the number of flips.

Tyler Moulton

Numerade Educator

Problem 9

Suppose that, for any given year, the probabilities that the stock market declines, that women's hemlines are lower, and
that both events occur are, respectively, $0.4,0.35,$ and $0.3 .$ Are the two events independent?
(A) Yes, because $(0.4)(0.35) \neq 0.3 .$
(B) No, because $(0.4)(0.35) \neq 0.3$.
(C) Yes, because $0.4>0.35>0.3$.
(D) No, because $0.5(0.3+0.4)=0.35$.
(E) There is insufficient information to answer this
question.

Tyler Moulton

Numerade Educator

Problem 10

Suppose that in a certain part of the world, in any 5o-year period the probability of a major plague is $0.39,$ the probability of a major famine is $0.52,$ and the probability of both a plague and a famine is $0.15 .$ What is the probability a famine given that there is a plague?
(A) $0.39-0.15$
(B) $\frac{0.15}{0.52}$
(C) $0.52-0.15$
(D) $\frac{0.15}{0.52}$
(E) $0.39+0.52-0.15$

Tyler Moulton

Numerade Educator

Problem 11

Suppose that $2 \%$ of a clinic's patients are known to have cancer. A blood test is developed that is positive in $98 \%$ of patients with cancer but is also positive in $3 \%$ of patients who do not have cancer. If a person who is chosen at random from the clinic's patients is given the test and it comes out positive, what is the probability that the person actually has cancer?
(A) 0.02
(B) $0.02+0.03$
$(\mathrm{C})(0.02)(0.98)$
(D) $(0.02)(0.98)+(0.98)(0.03)$
(E) $\frac{(0.02)(0.98)}{(0.02)(0.98)+(0.98)(0.03)}$

Bryan Meares

Numerade Educator