Conditional Probability: Master the Basics with Interactive Quizzes

Question 1

Which of the following scenarios best exemplifies conditional probability?

Accepted Answer

Estimating the likelihood of a patient recovering from a surgery

Answer

Predicting the weather forecast for tomorrow

Answer

Determining the probability of winning the lottery

Answer

Calculating the average height of a population

Question 2

Which of the following questions illustrates a conditional probability scenario?

Accepted Answer

What is the probability of rolling a 6 on a dice, given that the previous roll was a 5?

Answer

What is the probability of rolling a 6 on a dice?

Answer

What is the probability of rolling a 6 on a dice and a 5 on a second dice?

Answer

What is the probability of rolling a 6 on a dice or a 5 on a second dice?

Question 3

In nursing, how is conditional probability used in risk assessment?

Accepted Answer

Estimating the likelihood of a patient developing a complication based on their medical history

Answer

Determining the probability of a specific diagnosis based only on symptoms

Answer

Calculating the odds of a treatment being effective for all patients with a particular condition

Question 4

Which of the following statements is NOT a property of conditional probability?

Accepted Answer

P(A|B) = 0 if P(B) ≠ 0

Answer

P(A|B) ≤ P(A)

Answer

P(A|B) = P(B|A) if and only if P(A) = P(B)

Answer

P(A|B) = 1 if P(B) = 0

Question 5

A hospital has a success rate of 80% in treating patients with a certain illness. If two patients enter the hospital with the same illness, what is the probability that at least one of them will be treated successfully?

Accepted Answer

96%

Answer

64%

Answer

80%

Question 6

A bag contains 6 blue marbles, 4 red marbles, and 3 green marbles. Two marbles are drawn randomly with replacement. What is the probability that at least one of the marbles drawn is blue?

Accepted Answer

39 / 45

Answer

6 / 135

Answer

1 / 4

Answer

18 / 135

Question 7

Which of the following accurately represents the formula for conditional probability?

Accepted Answer

P(A|B) = P(A ∩ B) / P(B)

Answer

P(A|B) = P(A) / P(B)

Answer

P(A|B) = P(B) / P(A)

Question 8

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue given that it is not red?

Accepted Answer

3/8

Answer

1/2

Answer

1/8

Answer

1/4

Question 9

A medical test has a sensitivity of 90% and a specificity of 80%. If the prevalence of the disease in the population is 5%, what is the probability that a person who tests positive actually has the disease?

Accepted Answer

36%

Answer

10%

Answer

50%

Question 10

A study found that 60% of patients who received a new medication experienced a reduction in symptoms. If 40% of patients in the study received the medication, what is the probability that a patient who experienced a reduction in symptoms received the medication?

Accepted Answer

0.75

Answer

0.50

Answer

0.25

Answer

1.00

Question 11

In conditional probability, what is the complement of event "A"?

Accepted Answer

not A

Answer

B

Answer

A or B

Question 12

A hospital has a policy that requires COVID-19 testing for all admitted patients. If the test has a sensitivity of 98% and a specificity of 95%, what is the probability that a patient who tests negative does not have COVID-19?

Accepted Answer

99.5%

Answer

100.0%

Answer

95.0%

Answer

98.0%

Question 13

A medical test correctly identifies 95% of patients with a specific disease and 90% of patients without the disease. If 2% of the population has the disease, what is the probability that a randomly selected person who tests positive actually has the disease?

Accepted Answer

0.17

Answer

0.05

Answer

0.95

Answer

0.90

Question 14

A survey of 200 college students found that 60% of them own a laptop, 40% own a tablet, and 20% own both a laptop and a tablet. If a student is selected randomly, what is the probability that the student owns a tablet given that they own a laptop?

Accepted Answer

0.67

Answer

0.20

Answer

0.80

Answer

0.50

Question 15

A manufacturer produces two types of light bulbs: Type A and Type B. Type A bulbs have a lifespan of 1000 hours, and Type B bulbs have a lifespan of 1500 hours. If 60% of the bulbs produced are Type A and 40% are Type B, what is the probability that a randomly selected bulb has a lifespan of 1000 hours?

Accepted Answer

0.6

Answer

0.5

Answer

0.3

Answer

0.4

Question 16

A genetic test is used to determine the probability of a person developing a certain disease. The test result is either positive or negative. If a person has the disease, the probability that the test result is positive is 0.9. If a person does not have the disease, the probability that the test result is negative is 0.8. What is the probability that a person who tests negative for the disease actually has the disease?

Accepted Answer

0.02

Answer

0.90

Answer

0.50

Answer

0.25

Question 17

A company wants to assess the effectiveness of a new training program. They conduct a survey among employees who completed the program. If 70% of employees who participated in the program reported an improvement in their performance, and 30% of employees did not participate in the program, what is the probability that a randomly selected employee who did not report an improvement in their performance participated in the program?

Accepted Answer

0.18

Answer

0.30

Answer

0.70

Answer

0.82

Question 18

A hospital has a 90% success rate for a particular surgery. If there are 100 surgeries performed each week, on average, about how many surgeries can be expected to be successful?

Accepted Answer

90

Answer

10

Answer

900

Answer

100

Question 19

Which of the following is NOT a property of conditional probability?

Accepted Answer

P(A|B) > P(A)

Answer

P(A|B) can range from 0 to 1

Answer

P(A|B) = 0 if P(B) = 0

Answer

P(A|B) = P(A) if A and B are independent

Question 20

The probability of developing a certain disease is 0.05. A screening test for the disease has a sensitivity of 0.9 and a specificity of 0.8. What is the probability that a randomly selected person who tests positive actually has the disease?

Accepted Answer

0.364

Answer

0.8

Answer

0.045

Answer

0.9

Question 21

Which of the following is the formula for Bayes' theorem?

Accepted Answer

P(A|B) = (P(B|A) * P(A)) / P(B)

Answer

P(A|B) = P(B) / P(A)

Answer

P(A|B) = P(A) - P(B)

Answer

P(A|B) = P(A) + P(B)