Probability - Conditional Probability

Grade 12 Maths Higher — Probability - Conditional Probability: 25 practice questions with instant scoring and explanations.

1. If P(A) = 0.4 and P(B|A) = 0.5, what is P(A ∩ B)?
2. If P(A ∩ B) = 0.3 and P(B) = 0.6, what is P(A|B)?
3. Two cards are drawn successively without replacement from a pack of 52 cards. What is the probability that both are aces?
4. If A and B are independent events with P(A) = 0.3 and P(B) = 0.4, what is P(A ∩ B)?
5. P(A) = 0.6, P(B) = 0.5 and P(A|B) = 0.4. Find P(A ∪ B).
6. A bag contains 3 red and 5 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?
7. If P(A') = 0.7, P(B) = 0.7 and P(B|A) = 0.5, find P(A|B).
8. If P(A ∪ B) = 0.8, P(A) = 0.5 and P(B) = 0.4, what is P(A ∩ B)?
9. Events A and B are such that P(A) = 1/2, P(A ∪ B) = 3/5, P(B) = p. What is p if A and B are independent?
10. A die is thrown twice. What is the probability that at least one of the throws shows 5?
11. The probability of solving a problem by A is 1/3 and by B is 1/5. What is the probability that the problem is solved if both try independently?
12. If P(A) = 0.4, P(B|A) = 0.3, find P(A' ∩ B') given A and B are independent.
13. A box has 4 defective and 6 good items. Two are drawn without replacement. P(both defective)?
14. If P(A) = 0.5, P(B) = 0.6, P(A ∩ B) = 0.3, find P(A|B').
15. In a class, 60% students play cricket and 40% play football. 30% play both. A student is selected at random who plays cricket. What is the probability they also play football?
16. Three coins are tossed simultaneously. What is the probability of getting at least 2 heads?
17. A and B are events where P(A) = 0.3, P(B) = 0.5. If A and B are mutually exclusive, what is P(A|B)?
18. If P(E₁) = 0.35, P(E₂) = 0.45 and P(E₁ ∪ E₂) = 0.65, find P(E₁|E₂).
19. A card is drawn from a well-shuffled pack. What is the probability that it is a king given that it is a face card?
20. An urn has 5 red and 3 black balls. Two are drawn one after another without replacement. P(second is red | first is red)?
21. If A and B are independent, P(A) = p and P(B) = 2p and P(exactly one occurs) = 5/9, then p = ?
22. P(A ∩ B') = 0.2 and P(A) = 0.5. Find P(B|A).
23. Two events are such that P(A) = 0.3, P(A ∪ B) = 0.65. If A and B are independent, find P(B).
24. A biased coin with P(H) = 0.6 is tossed 3 times. P(at least 2 heads)?
25. If P(A) = 0.4, P(B) = 0.5, and P(A ∪ B) = 0.7, are A and B independent?