Advanced MCQ on Conditional Probability (Download PDF)







Conditional probability is the probability of an event occurring given that another event has already occurred. It quantifies how the likelihood of one event changes when we know that another event is true. Mathematically, the conditional probability of event A given event B is expressed as P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events occurring, and P(B) is the probability of event B. Conditional probability is fundamental in fields like statistics, risk assessment, and machine learning, helping to model dependent events and make informed decisions based on existing information. This is an advanced Conditional Probability MCQ with Answer Key. You can download this MCQ from the link provided in the result page.

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1. 
Given that P(A)=0.4, P(B)=0.5P, and P(A∩B)=0.2, what is P(A∣B)?

2. 
In a factory, 60% of the products are made by Machine A and 40% by Machine B. Machine A produces 5% defective items, and Machine B produces 10% defective items. If a product is found to be defective, what is the probability it was made by Machine A?

3. 
If P(B∣A)=0.6 and P(A)=0.5, and the events are independent, what is P(B)?

4. 
A company has two types of employees: Type A and Type B. 70% of the employees are Type A, and 30% are Type B. The probability that a Type A employee completes a task successfully is 0.9, and the probability that a Type B employee completes the task successfully is 0.8. Given that an employee successfully completed the task, what is the probability that the employee is Type A?

5. 
In a certain test, 70% of students passed Mathematics, 60% passed English, and 50% passed both. If a student is known to have passed Mathematics, what is the probability that they also passed English?

6. 
In a game, the probability of winning at stage 1 is 0.4. If a player wins at stage 1, the probability of winning at stage 2 is 0.7. What is the conditional probability of winning at stage 2 given that the player wins at stage 1?

7. 
A car manufacturing plant has two assembly lines, A and B. 70% of cars come from line A and 30% from line B. If a defect is found, the probability that it came from line A is 0.8. What is the probability that a car selected at random is defective?

8. 
A student studies 3 subjects: Mathematics, Physics, and Chemistry. The probability of passing Mathematics is 0.7, Physics is 0.8, and Chemistry is 0.6. What is the probability that a student passed Mathematics given that they passed both Physics and Chemistry?

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