Loading test…

AP Statistics Unit 4: Probability, Random Variables, and Probability Distributions

12 questions

Header banner

Unit 4: Probability, Random Variables, and Probability Distributions

0 of 12 answered

~7 min left

Question 1

A fair coin is flipped 8 times. Using the binomial distribution, what is the probability of getting exactly 5 heads?

\frac{5}{8} = 0.625

(5 8) (0.5)^{5} (0.5)^{3} = \frac{56}{256} \approx 0.219

(0.5)^{8} \approx 0.004

(5 8) (0.5)^{8} \approx 0.219

is wrong; the correct answer is 0.273.

Question 2

In a standard deck of 52 cards, two cards are drawn without replacement. Given that the first card drawn is an ace, what is the probability that the second card is also an ace?

\frac{4}{52}

\frac{1}{17}

\frac{4}{51}

\frac{3}{52}

Question 3

Events $A$ and $B$ are mutually exclusive with $P (A) = 0.30$ and $P (B) = 0.45$ . What is $P (A or B)$ ?

A.0.135B.0.75C.0.775D.1.00

Question 4

Events $A$ and $B$ satisfy $P (A) = 0.4$ , $P (B) = 0.5$ , and $P (A \cap B) = 0.2$ . Are $A$ and $B$ independent?

A.Yes, because

P (A) + P (B) = 0.9

and

P (A \cap B) > 0

.B.Yes, because

P (A \cap B) = P (A) \cdot P (B)

.C.No, because

P (A \cap B) \neq = 0

.D.No, because

P (A ∣ B) \neq = P (A)

Question 5

A candy machine has a 30% chance of dispensing a rare flavor. You try the machine 10 times. Using the binomial model, what is the probability of getting the rare flavor at least once?

1 - (0.30)^{10}

10 \times 0.30 = 0.30

1 - (0.70)^{10} \approx 0.972

(0.30)^{1} (0.70)^{9} \approx 0.121

In-content ad

Question 6

A student guesses randomly on a 5-question true/false quiz. Let $X$ = number of correct answers. What are the mean and standard deviation of $X$ ?

μ = 2.5

σ = 1.25

μ = 2.5

σ \approx 1.12

μ = 5

σ = 2.5

μ = 0.5

σ = 0.5

Question 7

A geometric random variable $X$ counts the number of trials until the first success, where $p = 0.25$ . What is $P (X = 3)$ ?

0.2 5^{3} \approx 0.016

(0.75)^{2} (0.25) \approx 0.141

(0.75)^{3} \approx 0.422

(1 3) (0.25)^{1} (0.75)^{2} \approx 0.422

Question 8

Two independent random variables $X$ and $Y$ have means $μ_{X} = 10$ , $μ_{Y} = 6$ , and standard deviations $σ_{X} = 3$ , $σ_{Y} = 4$ . What are the mean and standard deviation of $X + Y$ ?

μ = 16

σ = 7

μ = 16

σ = 5

μ = 4

σ = 5

μ = 16

σ = 25

Question 9

A student claims that because $P (A) = 0.5$ and $P (B) = 0.4$ , events $A$ and $B$ cannot both occur since $P (A) + P (B) = 0.9 < 1$ . Is this reasoning valid?

A.Yes; if

P (A) + P (B) < 1

, they must be mutually exclusive.B.No;

P (A) + P (B) < 1

does not prevent both events from occurring simultaneously.C.Yes; the sum of individual probabilities must equal 1 for events to overlap.D.No; events can co-occur only if

P (A) + P (B) > 1

Question 10

A bag contains 4 red marbles and 6 blue marbles. One marble is drawn at random. What is the probability of drawing a red marble?

A.0.40B.0.60C.0.44D.0.67

In-content ad

Question 11

A discrete random variable $X$ has the probability distribution shown. What is $E (X)$ ?

$x$	1	2	3	4
$P (X = x)$	0.10	0.30	0.40	0.20

A.2.50B.2.70C.3.00D.1.00

Question 12

In a large population, 1% of people have a certain disease. A test has a sensitivity of 95% (true positive rate) and a specificity of 90% (true negative rate). A randomly selected person tests positive. What is the approximate probability they actually have the disease?

A.About 95%B.About 87%C.About 8.7%D.About 1%

AP Statistics Unit 4: Probability, Random Variables, and Probability Distributions — Free with Answer Explanations | Test Practice Hub