AP®StatisticsCollege BoardExam QuestionsUnit 2: Probability, Random Variables, and Probability DistributionsDiscrete Random Variables

Discrete Random Variables (College Board AP® Statistics): Exam Questions

Syllabus Edition

First teaching 2026

First exams 2027

3 mins3 questions

1 mark

At the end of a level in a video game, a player can score 0, 10, 50, or 100 points. Let the random variable $X$ represent the number of points scored by a player at the end of a level. The expected value of $X$ is 15.5 points. What is the meaning of the expected value in this context?

Every player will score 15.5 points at the end of the level.
Players score an average of 15.5 points at the end of the level.
15.5 percent of all players will score 100 points.
A score of 100 points is the most likely outcome.

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1 mark

Sun and Jin sit next to each other on a flight. There is a 60 percent chance that Sun will fall asleep during the flight. If Sun falls asleep, there is a 70 percent chance that Jin will also fall asleep. If Sun does not fall asleep, there is a 20 percent chance that Jin will fall asleep. Let $X$ be the number of them that fall asleep during the flight.

Which of the following tables shows the probability distribution of $X$ ?

$x$
$0$
$1$
$2$
$P (x)$
$\frac{1}{4}$
$\frac{1}{2}$
$\frac{1}{4}$
$x$
$0$
$1$
$2$
$P (x)$
$0.32$
$0.26$
$0.42$
$x$
$0$
$1$
$2$
$P (x)$
$0.32$
$0.08$
$0.42$
$x$
$0$
$1$
$2$
$P (x)$
$0.60$
$0.20$
$0.70$

$x$	$0$	$1$	$2$
$P (x)$	$\frac{1}{4}$	$\frac{1}{2}$	$\frac{1}{4}$

$x$	$0$	$1$	$2$
$P (x)$	$0.32$	$0.26$	$0.42$

$x$	$0$	$1$	$2$
$P (x)$	$0.32$	$0.08$	$0.42$

$x$	$0$	$1$	$2$
$P (x)$	$0.60$	$0.20$	$0.70$

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