Unit 12 · Test

Unit 12 test: Probability

15 questions. Answer them all, then submit to see your score. Solutions unlock after you submit.

This test covers sample spaces and the addition rule, independent events, conditional probability, two-way tables, and permutations and combinations.

Question 1

You roll two number cubes. What is the probability that the sum is $9$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 2

You draw one card from a standard $52$ -card deck. What is the probability that it is red or an ace?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 3

Events $A$ and $B$ are independent, with $P(A) = 0.7$ and $P(B) = 0.2$ . Find $P(A \cap B)$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 4

$P(A) = 0.5$ , $P(B) = 0.3$ and $P(A \cap B) = 0.15$ . Which statement is true?

Question 5

You roll a number cube $3$ times. What is the probability of rolling at least one $6$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 6

$P(B) = 0.6$ and $P(A \cap B) = 0.18$ . Find $P(A \mid B)$ .

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 7

A bag has $3$ red and $7$ blue marbles. Two marbles are drawn without replacement. What is the probability that both are blue?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 8

You roll two number cubes. Given that the sum is $7$ , what is the probability that one of the cubes shows a $1$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Problems 9–12 use this survey of $200$ students about how they get to school.

	Walk	Bus	Car	Total
Freshmen	$20$	$45$	$15$	$80$
Seniors	$30$	$25$	$65$	$120$
Total	$50$	$70$	$80$	$200$

Question 9

A student is chosen at random. What is $P(\text{bus})$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 10

What is $P(\text{senior} \mid \text{car})$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 11

What is $P(\text{car} \mid \text{senior})$ ?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 12

Is riding the bus independent of being a freshman?

Question 13

A club of $9$ members chooses a president, vice president, secretary and treasurer. No one can hold two offices. In how many ways can the offices be filled?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 14

How many ways are there to choose $4$ students from a group of $12$ to go on a field trip?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.

Question 15

A committee of $3$ is chosen at random from $6$ juniors and $4$ seniors. What is the probability that all $3$ members are juniors?

Enter a number. Fractions like 3/4 and sqrt(2) are OK.