Advanced Probability & Statistics Quiz

1. A bag contains 4 red and 6 blue balls. One is drawn and not replaced, then another is drawn. What is P(both red)?

1. 16/100
2. 2/15
3. 4/25
4. 8/90

2. What is 'conditional probability' P(A|B)?

1. The probability of A and B both happening
2. The probability of A given that B has already occurred
3. The probability of A or B happening
4. The probability of neither A nor B

3. Two events A and B are independent. P(A) = 0.3 and P(B) = 0.4. What is P(A and B)?

1. 0.1
2. 0.12
3. 0.58
4. 0.7

4. P(A) = 0.5, P(B) = 0.4, P(A or B) = 0.7. Are A and B mutually exclusive?

1. No, because P(A or B) ≠ P(A) + P(B)
2. No, there is not enough information
3. Yes, because P(A or B) ≠ P(A) + P(B)
4. Yes, because P(A) + P(B) = 0.9 and P(A or B) = 0.7

5. What is the formula P(A or B) for non-mutually exclusive events?

1. P(A) + P(B)
2. P(A) + P(B) − P(A and B)
3. P(A) × P(B)
4. P(A) − P(B) + P(A and B)

6. A fair coin is flipped three times. What is P(all three heads)?

1. 1/2
2. 1/4
3. 1/6
4. 1/8

7. A box contains 3 white, 4 red, and 5 blue balls. What is P(not blue)?

1. 1/2
2. 5/12
3. 5/7
4. 7/12

8. What does the standard deviation measure?

1. How spread out the data is from the mean
2. The difference between the highest and lowest values
3. The middle value of a data set
4. The most common value

9. The data set is 2, 4, 4, 4, 5, 5, 7, 9. What is the mean?

1. 4
2. 4.5
3. 5
4. 5.5

10. From a class of 30, P(a randomly chosen student likes maths) = 2/5. How many students like maths?

1. 10
2. 12
3. 15
4. 18

11. What is a 'tree diagram' used for in probability?

1. Calculating the mean of a data set
2. Displaying data as a bar chart
3. Showing all possible outcomes of a sequence of events with their probabilities
4. Showing the frequency of different categories

12. What is the interquartile range (IQR)?

1. Half the range
2. The difference between the upper quartile (Q3) and lower quartile (Q1)
3. The full range of the data
4. The range of the middle 25% of data

13. Data: 3, 7, 7, 2, 9, 1, 5. Find the median.

1. 4.86
2. 5
3. 6
4. 7

14. A two-way table shows 200 students. 80 are boys; 60 of the 200 play chess; 20 boys play chess. What is P(a randomly chosen student is a girl who does not play chess)?

1. 100/200
2. 60/120
3. 60/200
4. 80/200

15. What is the probability of rolling a sum of 7 with two fair dice?

1. 1/6
2. 5/36
3. 6/36
4. 7/36

16. What is a 'box plot' (box-and-whisker diagram) used to display?

1. A frequency distribution as a histogram
2. The correlation between two variables
3. The mean and standard deviation
4. The minimum, Q1, median, Q3, and maximum of a data set

17. A card is drawn from a standard 52-card deck. What is P(drawing a king or a heart)?

1. 1/4
2. 16/52
3. 17/52
4. 4/13

18. What does it mean for two events to be mutually exclusive?

1. One causes the other
2. They always happen together
3. They are equally likely
4. They cannot both happen at the same time

19. The mean of 5 numbers is 12. Four of the numbers are 10, 14, 8, 16. What is the fifth number?

1. 10
2. 12
3. 14
4. 16

20. In a class, 40% of students passed maths and 30% passed science. 15% passed both. What percentage passed at least one?

1. 45%
2. 55%
3. 70%
4. 85%