DSE 數學科：概率與排列組合

1. A fair six-faced die is rolled once. What is the probability that the result is a prime number?

2. P(A) = 0.4, P(B) = 0.5 and P(A ∩ B) = 0.2. What is P(A ∪ B)?

3. If A and B are mutually exclusive, which statement must be true?

4. A and B are independent, with P(A) = 0.5 and P(B) = 0.4. What is P(A ∩ B)?

5. In how many ways can 3 students be chosen from 8, if the order of selection does not matter?

6. In how many ways can 5 distinct books be arranged in a row?

7. A password is an ordered pair of distinct letters chosen from A, B, C, D and E. How many passwords are there?

8. A bag has 3 red and 2 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

9. P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.2. What is P(A | B)?

10. A and B are mutually exclusive, and both have positive probability. They

11. How many 3-digit numbers can be formed from the digits 1, 2, 3 and 4 if no digit is repeated?

12. In a group, 40% are girls. 30% of the girls and 20% of the boys play the piano. A piano player is chosen at random. What is the probability that this player is a girl?