Probability – Conditional, Bayes, Random Variables & Distributions Quiz - ICSE Class 12 Mathematics
Free practice quiz: Probability – Conditional, Bayes, Random Variables & Distributions (ICSE Class 12 Mathematics). 25 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
Play all 25 questions freeSample questions
Two events A and B are such that P(A) = 1/2, P(B) = 1/3, and P(A ∩ B) = 1/4. What is P(A' ∪ B')?
- 1/4
- 3/4
- 1/2
- 5/6
Show answer
Answer: B. 3/4
We know that P(A' ∪ B') = P((A ∩ B)'). Using the complement rule, P((A ∩ B)') = 1 - P(A ∩ B). Given P(A ∩ B) = 1/4, so P(A' ∪ B') = 1 - 1/4 = 3/4.
Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.5, what is P(A ∪ B)?
- 0.7
- 0.9
- 0.2
- 1.0
Show answer
Answer: A. 0.7
For independent events, P(A ∩ B) = P(A) * P(B). So, P(A ∩ B) = 0.4 * 0.5 = 0.2. The formula for P(A ∪ B) is P(A) + P(B) - P(A ∩ B). Therefore, P(A ∪ B) = 0.4 + 0.5 - 0.2 = 0.7.
Suppose P(E) = 0.4 and P(F) = 0.3. If E and F are mutually exclusive events, what is P(E ∪ F)?
- 0.1
- 0.7
- 0.12
- 0.3
Show answer
Answer: B. 0.7
For mutually exclusive events, P(E ∩ F) = 0. The formula for P(E ∪ F) is P(E) + P(F) - P(E ∩ F). Therefore, P(E ∪ F) = 0.4 + 0.3 - 0 = 0.7.
Two events A and B are such that P(A|B) = 0.7 and P(B|A) = 0.4. If P(A) = 0.5, find P(B).
- 0.286
- 0.35
- 0.571
- 0.2
Show answer
Answer: A. 0.286
We know P(A|B) = P(A ∩ B) / P(B) and P(B|A) = P(A ∩ B) / P(A). From the second equation, P(A ∩ B) = P(B|A) * P(A) = 0.4 * 0.5 = 0.2. Now substitute this into the first equation: 0.7 = 0.2 / P(B). Therefore, P(B) = 0.2 / 0.7 = 2/7. Approximately, 2/7 ≈ 0.2857, which rounds to 0.286.
Suppose P(A) = 0.3 and P(B) = 0.4. If events A and B are mutually exclusive, what is P(A ∩ B)?
- 0
- 0.1
- 0.7
- 0.12
Show answer
Answer: A. 0
For mutually exclusive events, the occurrence of one event excludes the occurrence of the other. Therefore, the probability of both events occurring simultaneously, P(A ∩ B), is 0.