Free Practice Quiz Question List

3 Conditional Probability and Independence Online Quiz Questions

Use this free practice quiz with 20 questions to review 3 Conditional Probability and Independence, test your knowledge, and prepare for your next test or exam.

20 questions

True or false

1 point

True or false: In general, conditional probability is directional, so $P(A\mid B)$ and $P(B\mid A)$ can have different values.

A
True
B
False

Choose one

1 point

In a survey, 30% of students study music, 20% study art, and 8% study both. What is $P(\text{music}\mid\text{art})$ ?

A
0.08
B
0.40
C
0.60
D
0.80

Choose one

1 point

A box contains 5 red balls and 3 blue balls. Two balls are drawn without replacement. What is the probability that both balls are red?

A
$\frac{5}{8}$
B
$\frac{4}{7}$
C
$\frac{5}{14}$
D
$\frac{25}{64}$

Choose one

1 point

A product comes from Source A with probability 0.60 and has a defect probability of 0.01 given Source A. It comes from Source B with probability 0.40 and has a defect probability of 0.04 given Source B. What is the overall probability that a randomly selected product is defective?

A
0.018
B
0.022
C
0.025
D
0.050

Choose all

1 point

Which statements are required for a collection of events to be a partition of the sample space? Select all correct answers.

A
The events are pairwise disjoint.
B
The events must all have equal probabilities.
C
Their union is the entire sample space.
D
Each event has a well-defined probability.

Choose all

1 point

Which quantities are needed to apply $P(A\mid B)=\frac{P(B\mid A)P(A)}{P(B)}$ ? Select all correct answers.

A
A prior probability such as $P(A)$
B
A likelihood such as $P(B\mid A)$
C
The requirement that A and B be independent
D
The evidence probability $P(B)$

True or false

1 point

True or false: Two mutually exclusive events with positive probabilities are dependent.

A
True
B
False

True or false

1 point

True or false: If three events are pairwise independent, then they must be mutually independent.

A
True
B
False

Written response

1 point

Given $P(A\cap B)=0.18$ and $P(B)=0.30$ , enter $P(A\mid B)$ as a decimal.

Written response

1 point

What term names the probability assigned after new evidence has been used to update an initial probability?

Fill in the blank

1 point

If $P(A\cap B)=P(A)P(B)$ , then A and B are . If this equality fails, they are .

Fill in the blank

1 point

The formula $P(A\cap B)=P(B)P(A\mid B)$ is the . In $P(A\mid B)$ , the quantity after the vertical bar indicates a probability.

Open ended

1 point

Explain why a partition $B_1,\ldots,B_k$ leads to the law of total probability $P(A)=\sum_{i=1}^{k}P(A\mid B_i)P(B_i)$ . Include the key set decomposition and probability rule.

Choose one

1 point

Events $B_1,\ldots,B_k$ form a partition. Which expression correctly gives $P(B_j\mid A)$ in the expanded form of Bayes’ theorem?

A
$P(B_j\mid A)=P(A\mid B_j)P(B_j)$
B
$P(B_j\mid A)=\frac{P(B_j)}{P(A\mid B_j)}$
C
$P(B_j\mid A)=\frac{P(A\mid B_j)P(B_j)}{\sum_{i=1}^{k}P(A\mid B_i)P(B_i)}$
D
$P(B_j\mid A)=\sum_{i=1}^{k}P(A\mid B_i)P(B_i)$

Choose one

1 point

Which formula defines the conditional probability of event $A$ given event $B$ , assuming $P(B)>0$ ?

A
$P(A\mid B)=\frac{P(A\cap B)}{P(A)}$
B
$P(A\mid B)=\frac{P(A\cap B)}{P(B)}$
C
$P(A\mid B)=P(A)+P(B)$
D
$P(A\mid B)=P(A)P(B)$

Choose one

1 point

A box contains 5 red balls and 3 blue balls. Two balls are drawn without replacement. What is the probability that both balls are red?

A
$\frac{5}{8}$
B
$\frac{4}{7}$
C
$\frac{5}{14}$
D
$\frac{25}{64}$

Choose one

1 point

Products come from three factories. Factory 1 supplies 50% with a 2% defect rate, Factory 2 supplies 30% with a 3% defect rate, and Factory 3 supplies 20% with a 5% defect rate. What is the overall probability that a randomly selected product is defective?

A
0.020
B
0.025
C
0.029
D
0.050

Choose one

1 point

Products come from three factories. Factory 1 supplies 50% with a 2% defect rate, Factory 2 supplies 30% with a 3% defect rate, and Factory 3 supplies 20% with a 5% defect rate. A product is known to be defective. What is the probability that it came from Factory 3? Give the value to four decimal places.

A
0.2000
B
0.2500
C
0.3448
D
0.5000

Written response

1 point

Among students, 40% take statistics and 15% take both statistics and computer science. What is $P(\text{computer science}\mid\text{statistics})$ ? Enter the probability as a decimal.

Written response

1 point

Suppose $P(A)=0.50$ , $P(B\mid A)=0.40$ , and $P(C\mid A\cap B)=0.30$ . What is $P(A\cap B\cap C)$ ? Enter the probability as a decimal.