Gaokao Exam Mathematics: Probability and Statistics

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?

Accepted Answer

3/8

Answer

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?

Accepted Answer

8

Answer

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)?

Accepted Answer

0.70

Answer

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?

Accepted Answer

1/6

Answer

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?

Accepted Answer

9

Answer

Total sum = 5 × 10 = 50; fifth number = 50 − (8+9+11+13) = 50 − 41 = 9.

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