Gaokao Exam Mathematics: Probability and Statistics 1 — Questions and Answers
Question 1: A bag contains 3 red balls and 5 blue balls. If one ball is drawn at random, what is the probability of drawing a red ball?
- 1/4
- 3/8 (Correct answer)
- 5/8
- 3/5
Correct answer: 3/8
There are 3 red balls out of 8 total, so the probability is 3/8.
Question 2: In a dataset of 7 values — 2, 4, 6, 8, 10, 12, 14 — what is the median?
- 6
- 7
- 8 (Correct answer)
- 10
Correct answer: 8
When ordered, the middle (4th) value of 7 numbers is 8.
Question 3: If P(A) = 0.4 and P(B) = 0.3 and events A and B are mutually exclusive, what is P(A ∪ B)?
- 0.12
- 0.58
- 0.70 (Correct answer)
- 0.82
Correct answer: 0.70
For mutually exclusive events, P(A ∪ B) = P(A) + P(B) = 0.4 + 0.3 = 0.7.
Question 4: A fair six-sided die is rolled twice. What is the probability of getting a sum of 7?
- 1/9
- 1/6 (Correct answer)
- 5/36
- 7/36
Correct answer: 1/6
There are 6 favorable pairs (1+6, 2+5, 3+4, 4+3, 5+2, 6+1) out of 36 total outcomes, giving 6/36 = 1/6.
Question 5: The mean of five numbers is 10. If four of the numbers are 8, 9, 11, and 13, what is the fifth number?
- 7
- 9 (Correct answer)
- 10
- 11
Correct answer: 9
Total sum = 5 × 10 = 50; fifth number = 50 − (8+9+11+13) = 50 − 41 = 9.
Question 6: Which measure of central tendency is most affected by an extreme outlier in a dataset?
- Mode
- Median
- Mean (Correct answer)
- Range
Correct answer: Mean
The mean incorporates every value arithmetically, so a single extreme outlier can shift it significantly.
Gaokao Exam Mathematics: Probability and Statistics 1
A bag contains 3 red balls and 5 blue balls.
If one ball is drawn at random, what is the probability of drawing a red ball?