Advanced Probability & Statistics Quiz

Question 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)?

Accepted Answer

2/15

Answer

4/25

Answer

8/90

Answer

16/100

Question 2

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

Accepted Answer

The probability of A given that B has already occurred

Answer

The probability of A and B both happening

Answer

The probability of A or B happening

Answer

The probability of neither A nor B

Question 3

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

Accepted Answer

0.12

Answer

0.7

Answer

0.58

Answer

0.1

Question 4

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

Accepted Answer

No, because P(A or B) ≠ P(A) + P(B)

Answer

Yes, because P(A or B) ≠ P(A) + P(B)

Answer

Yes, because P(A) + P(B) = 0.9 and P(A or B) = 0.7

Answer

No, there is not enough information

Question 5

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

Accepted Answer

P(A) + P(B) − P(A and B)

Answer

P(A) + P(B)

Answer

P(A) × P(B)

Answer

P(A) − P(B) + P(A and B)

Question 6

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

Accepted Answer

1/8

Answer

1/2

Answer

1/4

Answer

1/6

Question 7

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

Accepted Answer

7/12

Answer

5/12

Answer

1/2

Answer

5/7

Question 8

What does the standard deviation measure?

Accepted Answer

How spread out the data is from the mean

Answer

The middle value of a data set

Answer

The difference between the highest and lowest values

Answer

The most common value

Question 9

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

Accepted Answer

5

Answer

4

Answer

4.5

Answer

5.5

Question 10

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

Accepted Answer

12

Answer

10

Answer

15

Answer

18

Question 11

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

Accepted Answer

Showing all possible outcomes of a sequence of events with their probabilities

Answer

Displaying data as a bar chart

Answer

Calculating the mean of a data set

Answer

Showing the frequency of different categories

Question 12

What is the interquartile range (IQR)?

Accepted Answer

The difference between the upper quartile (Q3) and lower quartile (Q1)

Answer

The full range of the data

Answer

The range of the middle 25% of data

Answer

Half the range

Question 13

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

Accepted Answer

5

Answer

7

Answer

4.86

Answer

6

Question 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)?

Accepted Answer

100/200

Answer

60/200

Answer

80/200

Answer

60/120

Question 15

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

Accepted Answer

6/36

Answer

1/6

Answer

7/36

Answer

5/36

Question 16

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

Accepted Answer

The minimum, Q1, median, Q3, and maximum of a data set

Answer

The mean and standard deviation

Answer

A frequency distribution as a histogram

Answer

The correlation between two variables

Question 17

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

Accepted Answer

16/52

Answer

17/52

Answer

4/13

Answer

1/4

Question 18

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

Accepted Answer

They cannot both happen at the same time

Answer

They always happen together

Answer

They are equally likely

Answer

One causes the other

Question 19

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

Accepted Answer

12

Answer

10

Answer

14

Answer

16

Question 20

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

Accepted Answer

55%

Answer

70%

Answer

85%

Answer

45%