10 questions · Form 4 Mathematics Bab 9: Probability of Combined Events
10 questions · plays in fullscreen
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Using the same bag (5 red, 3 green), if two marbles are drawn WITHOUT replacement, what is the probability that both are red?
Answer: B
P(1st Red) = 58. P(2nd Red | 1st Red) = 47. P(Both Red) = (58) × (47) = 2056 = 514.
2. 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.
3. Events X and Y are mutually exclusive. Given P(X) = 13 and P(Y) = 14, find P(X ∪ Y).
Answer: B
Since X and Y are mutually exclusive: P(X ∪ Y) = P(X) + P(Y) = 13 + 14 = 412 + 312 = 712.
4. A bag contains 5 red marbles and 3 green marbles. A marble is drawn, its color recorded, and REPLACED. A second marble is drawn. What is the probability of drawing two red marbles?
Answer: A
P(Red) = 58. Since drawing is with replacement, events are independent. P(Red and Red) = (58) × (58) = 2564.
5. Two events A and B are independent. If P(A) = 0.4 and P(B) = 0.5, find P(A ∩ B).
Answer: B
For independent events, P(A ∩ B) = P(A) × P(B) = 0.4 × 0.5 = 0.20.
6. 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.
7. 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.
8. A card is selected from a standard deck of 52 playing cards. Let A be getting a King and B be getting a Heart. Are events A and B mutually exclusive?
Answer: B
There is a card that is both a King and a Heart (King of Hearts), so P(A ∩ B) = 152 ≠ 0. They are not mutually exclusive.
9. 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.
10. A student takes two independent tests. Probability of passing Math is 0.8 and passing English is 0.9. Find the probability of passing Math but FAILING English.
Answer: B
P(Pass Math) = 0.8. P(Fail English) = 1 - 0.9 = 0.1. P(Pass Math ∩ Fail English) = 0.8 × 0.1 = 0.08.