Statistics and Probability Practice Questions
IB (International Baccalaureate) · IB Math AI SL · 141 free MCQs with instant results and detailed explanations.
141
Total
45
Easy
73
Medium
23
Hard
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Sample Questions from Statistics and Probability
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
A bag contains 4 red, 6 blue, and 10 green marbles. If one marble is drawn at random, what is the probability that it is blue?
A.
0.25
B.
0.30
C.
0.20
D.
0.40
Show Answer & Explanation
Correct Answer: B
The total number of marbles is 4 + 6 + 10 = 20. The probability of drawing a blue marble is the number of blue marbles (6) divided by the total number of marbles (20), which gives 6/20 = 0.30.
Q2
Easy
In a class of 30 students, 12 students play football, 8 play basketball, and 5 play both sports. How many students play only football?
A.
7
B.
8
C.
12
D.
5
Show Answer & Explanation
Correct Answer: A
To find students who play only football, we subtract those who play both sports from the total football players: 12 (football) - 5 (both) = 7 students play only football.
Q3
Easy
A student scores the following marks in 5 subjects: 70, 80, 90, 85, and 75. What is the mean score?
A.
78
B.
80
C.
82
D.
85
Show Answer & Explanation
Correct Answer: B
The mean score is calculated by adding all the scores and dividing by the number of subjects: (70 + 80 + 90 + 85 + 75) / 5 = 400 / 5 = 80.
Q4
Medium
A data set consists of the following values: 12, 15, 20, 22, 22, 25, 30. What is the median of this data set?
A.
22
B.
20
C.
25
D.
21
Show Answer & Explanation
Correct Answer: A
To find the median, order the data and identify the middle value. The ordered data is 12, 15, 20, 22, 22, 25, 30. The median is the fourth value, which is 22.
Q5
Medium
In a survey, 70% of students prefer online classes over traditional classes. If 200 students were surveyed, how many prefer online classes?
A.
140
B.
150
C.
120
D.
160
Show Answer & Explanation
Correct Answer: A
To find the number of students who prefer online classes, multiply the total number of students by the percentage: 200 * 70% = 200 * 0.7 = 140.
Q6
Medium
A box contains 4 red, 3 blue, and 5 green balls. If one ball is drawn at random, what is the probability that it is red?
A.
1/4
B.
1/3
C.
2/5
D.
1/2
Show Answer & Explanation
Correct Answer: B
The probability of drawing a red ball is the number of red balls divided by the total number of balls: P(Red) = 4/(4+3+5) = 4/12 = 1/3.
Q7
Medium
If two events A and B are independent, and P(A) = 0.3 and P(B) = 0.4, what is P(A and B)?
A.
0.12
B.
0.7
C.
0.1
D.
0.5
Show Answer & Explanation
Correct Answer: A
For independent events, P(A and B) = P(A) * P(B). Therefore, P(A and B) = 0.3 * 0.4 = 0.12.
Q8
Hard
A researcher wants to study the effect of a new teaching method on student performance. She randomly assigns 60 students to two groups: 30 in the control group using traditional methods and 30 in the experimental group using the new method. After a semester, the mean score of the control group is 75 with a standard deviation of 10, and the mean score of the experimental group is 82 with a standard deviation of 12. Using a two-sample t-test, what can the researcher conclude if the calculated t-value is 2.23 and the critical t-value at 58 degrees of freedom (ฮฑ=0.05) is approximately 2.00?
A.
Reject the null hypothesis; the new teaching method is effective.
B.
Fail to reject the null hypothesis; the new teaching method is ineffective.
C.
The results are inconclusive due to insufficient data.
D.
The two groups are not comparable due to unequal variances.
Show Answer & Explanation
Correct Answer: A
The calculated t-value of 2.23 exceeds the critical t-value of 2.00. This means we reject the null hypothesis in favor of the alternative, indicating that the new teaching method significantly improves student performance.
Q9
Hard
A researcher analyzes the heights of students in a school and finds that the mean height is 160 cm with a standard deviation of 10 cm. If the heights are normally distributed, what percentage of students is expected to be between 150 cm and 170 cm?
A.
68%
B.
95%
C.
84%
D.
50%
Show Answer & Explanation
Correct Answer: A
According to the empirical rule for normal distributions, approximately 68% of the data falls within one standard deviation from the mean. Here, 150 cm (mean - 1 SD) to 170 cm (mean + 1 SD) covers this range.
Q10
Hard
A bag contains 5 red, 3 blue, and 2 green marbles. If 3 marbles are drawn at random without replacement, what is the probability that exactly 2 are red?
A.
0.5
B.
0.28
C.
0.35
D.
0.18
Show Answer & Explanation
Correct Answer: B
To find the probability of drawing exactly 2 red marbles, we use the combination formula. The favorable outcomes (2 red, 1 not red) divided by total outcomes gives us the probability of 0.28.
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Statistics and Probability โ IB (International Baccalaureate) IB Math AI SL Practice Questions Online
This page contains 141 practice MCQs for the chapter Statistics and Probability in IB (International Baccalaureate) IB Math AI SL. The questions are organized by difficulty โ 45 easy, 73 medium, 23 hard โ so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.