Conditional Probability and Independence: Interactive Learning Quizzes

Question 1

A bag contains 5 red marbles and 3 blue marbles. What is the probability of drawing a red marble, given that the first marble drawn was blue and not replaced?

Accepted Answer

5/7

Answer

3/7

Answer

5/8

Answer

3/8

Question 2

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, what is P(A and B)?

Accepted Answer

0.24

Answer

0.1

Answer

1

Answer

0.7

Question 3

A fair coin is tossed twice. Let event A be 'getting heads on the first toss' and event B be 'getting tails on the second toss'. Are events A and B independent?

Accepted Answer

Yes

Answer

Cannot be determined

Answer

No

Answer

It depends on the outcome of the first toss

Question 4

A box contains 10 light bulbs, 3 of which are defective. If two bulbs are randomly selected without replacement, what is the probability that both are defective?

Accepted Answer

1/15

Answer

1/5

Answer

3/10

Answer

3/90

Question 5

A student is taking a multiple-choice exam with 10 questions, each having 4 options. If the student randomly guesses on each question, what is the probability of getting at least one question correct?

Accepted Answer

1 - (3/4)^10

Answer

10 * (1/4) * (3/4)^9

Answer

1/4

Answer

(3/4)^10

Question 6

A medical test for a disease has a 95% accuracy rate. If 1% of the population has the disease, what is the probability that a person actually has the disease given that they test positive?

Accepted Answer

0.19

Answer

0.95

Answer

0.05

Answer

0.01

Question 7

A box contains 4 red balls and 6 blue balls. Two balls are drawn randomly without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn was blue?

Accepted Answer

4/9

Answer

6/10

Answer

2/5

Answer

4/10

Question 8

A study found that 80% of people who use a certain medication experience relief from their symptoms. If 20% of the population uses the medication, what is the probability that a randomly selected person experiences relief from their symptoms?

Accepted Answer

0.16

Answer

0.8

Answer

1

Answer

0.2

Question 9

A die is rolled twice. What is the probability of getting a 6 on the first roll and an odd number on the second roll?

Accepted Answer

1/12

Answer

1/36

Answer

1/6

Answer

1/2