10 questions · Form 4 Mathematics Bab 9: Probability of Combined Events
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1. A box contains 3 red balls and 7 blue balls. A ball is drawn at random and NOT replaced. A second ball is then drawn. What type of events are these?
Answer: C
Because the first ball is not replaced, the composition of the box changes, affecting the probability of the second draw. Thus, they are dependent events.
2. In a class of 30 students, 18 study Physics, 12 study Chemistry, and 5 study both. A student is picked at random. What is the probability that the student studies Physics OR Chemistry?
Answer: A
P(P ∪ C) = P(P) + P(C) - P(P ∩ C) = 1830 + 1230 - 530 = 2530 = 56.
3. A box contains cards labeled with numbers 1 to 10. A card is drawn at random. Let A = prime numbers, B = multiples of 3. Find P(A ∪ B).
Answer: A
A = {2, 3, 5, 7} → 4 items. B = {3, 6, 9} → 3 items. A ∩ B = {3} → 1 item. A ∪ B = {2, 3, 5, 6, 7, 9} → 6 items? Wait: Prime numbers in 1-10 are 2, 3, 5, 7 (4 items). Multiples of 3 are 3, 6, 9 (3 items). Union = {2, 3, 5, 6, 7, 9} which is 6 items. P(A ∪ B) = 610 or 35. Option D is 610.
4. Which formula calculates the probability of union of two non-mutually exclusive events A and B?
Answer: C
For non-mutually exclusive events, overlapping outcomes counted twice must be subtracted: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
5. A single fair six-sided die is rolled. What is the probability of getting an even number OR a number greater than 4?
Answer: B
Even = {2, 4, 6} → P(Even) = 36. Greater than 4 = {5, 6} → P(>4) = 26. Both = {6} → P(Both) = 16. P(Union) = 36 + 26 - 16 = 46 = 23.
6. If events A and B are mutually exclusive, what is P(A ∩ B)?
Answer: B
Mutually exclusive events cannot occur simultaneously, so their intersection P(A ∩ B) = 0.
7. Two fair coins are tossed. What is the probability of getting two heads or two tails?
Answer: B
Sample space = {HH, HT, TH, TT}. Two heads = {HH}, Two tails = {TT}. They are mutually exclusive. P(HH or TT) = 14 + 14 = 24 = 12.
8. A spinner has 4 equal sectors colored Red, Blue, Green, Yellow. The spinner is spun twice. What is the probability of getting Green on the first spin AND Yellow on the second spin?
Answer: C
The spins are independent. P(Green) = 14, P(Yellow) = 14. P(Green ∩ Yellow) = 14 × 14 = 116.
9. A target is shot by Ali and Ahmad independently. Probability of Ali hitting is 0.6 and Ahmad hitting is 0.7. Find the probability that BOTH hit the target.
Answer: A
Independent events: P(Both hit) = P(Ali) × P(Ahmad) = 0.6 × 0.7 = 0.42.
10. If P(A ∪ B) = 0.75, what is the probability of the complement event P((A ∪ B)')?
Answer: A
P((A ∪ B)') = 1 - P(A ∪ B) = 1 - 0.75 = 0.25.