Statistics & Probability for Competitive Exam Success

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Statistics & Probability

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Statistics & Probability MCQ & Objective Questions

Statistics and Probability are crucial subjects for students preparing for various school and competitive exams in India. Mastering these topics not only enhances your analytical skills but also boosts your confidence in tackling exam questions. Practicing MCQs and objective questions is an effective way to solidify your understanding and improve your performance in exams. By focusing on important questions and practice questions, you can ensure a thorough preparation strategy.

What You Will Practise Here

Fundamental concepts of Statistics including mean, median, and mode
Probability theory and its applications in real-life scenarios
Understanding and interpreting various types of data distributions
Key formulas related to permutations and combinations
Graphical representation of data through charts and histograms
Statistical measures of dispersion such as variance and standard deviation
Concepts of conditional probability and independent events

Exam Relevance

Statistics and Probability are integral parts of the curriculum for CBSE, State Boards, NEET, and JEE. These topics frequently appear in the form of MCQs, where students are tested on their ability to apply concepts to solve problems. Common question patterns include calculating probabilities, interpreting data sets, and applying statistical formulas. Familiarity with these question types can significantly enhance your exam readiness.

Common Mistakes Students Make

Confusing the concepts of mean, median, and mode
Misunderstanding the difference between independent and dependent events
Overlooking the importance of units when calculating probabilities
Failing to interpret graphs and charts accurately
Neglecting to practice problems involving permutations and combinations

FAQs

Question: What are the key formulas I should remember for Statistics and Probability?
Answer: Important formulas include those for mean, median, mode, variance, standard deviation, and the basic probability formula P(A) = Number of favorable outcomes / Total outcomes.

Question: How can I improve my accuracy in solving Statistics and Probability MCQs?
Answer: Regular practice of objective questions and understanding the underlying concepts will help improve your accuracy and speed in solving MCQs.

Start solving practice MCQs today to test your understanding of Statistics and Probability. The more you practice, the better prepared you will be for your exams. Let's ace those important Statistics & Probability questions together!

Mean Median Mode Probability Rules Variance & SD

Q. A bag contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is not black?

A. 2/5
B. 1/5
C. 1/2
D. 4/10

Solution

Total balls = 4 + 6 = 10. Probability of not drawing a black ball = Number of white balls / Total balls = 4/10 = 2/5.

Correct Answer: A — 2/5

Q. A bag contains 4 white balls and 6 black balls. If one ball is drawn at random, what is the probability that it is not black?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

Total balls = 4 + 6 = 10. Probability of not drawing a black ball = Number of white balls / Total balls = 4/10 = 2/5.

Correct Answer: C — 4/5

Q. A bag contains 4 white balls and 6 black balls. If one ball is drawn at random, what is the probability that it is black?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

The total number of balls is 4 + 6 = 10. The number of black balls is 6. Therefore, the probability of drawing a black ball is 6/10 = 3/5.

Correct Answer: B — 3/5

Q. A bag contains 4 white, 3 black, and 5 red balls. If one ball is drawn at random, what is the probability that it is not black?

A. 1/4
B. 3/4
C. 5/12
D. 2/3

Solution

Total balls = 4 + 3 + 5 = 12. Non-black balls = 4 + 5 = 9. Probability = Non-black balls / Total balls = 9/12 = 3/4.

Correct Answer: B — 3/4

Q. A bag contains 4 white, 5 black, and 6 red balls. If one ball is drawn at random, what is the probability that it is not black?

A. 1/3
B. 2/3
C. 5/11
D. 7/11

Solution

Total balls = 4 + 5 + 6 = 15. Non-black balls = 4 + 6 = 10. Probability = Non-black balls / Total balls = 10/15 = 2/3.

Correct Answer: D — 7/11

Q. A bag contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? (2022)

A. 3/8
B. 5/8
C. 1/2
D. 1/3

Solution

Total balls = 5 + 3 = 8. Probability of red ball = Number of red balls / Total balls = 5/8.

Correct Answer: B — 5/8

Q. A box contains 10 balls numbered from 1 to 10. What is the probability of drawing a ball with an even number?

A. 1/2
B. 1/5
C. 1/10
D. 3/10

Solution

Even numbers in the box are 2, 4, 6, 8, 10 (5 even numbers). Total balls = 10. Probability = 5/10 = 1/2.

Correct Answer: A — 1/2

Q. A box contains 10 balls, 4 of which are red. If one ball is drawn at random, what is the probability that it is red? (2020)

A. 2/5
B. 1/2
C. 4/10
D. 3/10

Solution

Probability of drawing a red ball = Number of red balls / Total balls = 4/10 = 2/5.

Correct Answer: B — 1/2

Q. A box contains 10 balls, 4 of which are white. If one ball is drawn at random, what is the probability that it is not white? (2022)

A. 2/5
B. 3/5
C. 1/2
D. 1/4

Solution

Number of non-white balls = 10 - 4 = 6. Probability = 6/10 = 3/5.

Correct Answer: B — 3/5

Q. A box contains 10 balls, of which 4 are red and 6 are blue. If one ball is drawn, what is the probability that it is not red?

A. 2/5
B. 3/5
C. 4/5
D. 1/5

Solution

Probability of not red = Number of non-red balls / Total balls = 6/10 = 3/5.

Correct Answer: B — 3/5

Q. A box contains 10 balls, of which 4 are white and 6 are black. If one ball is drawn, what is the probability that it is black?

A. 3/5
B. 2/5
C. 1/2
D. 1/10

Solution

Probability = Number of black balls / Total balls = 6/10 = 3/5.

Correct Answer: A — 3/5

Q. A box contains 10 balls, of which 4 are white and 6 are black. If one ball is drawn at random, what is the probability that it is white?

A. 2/5
B. 3/5
C. 4/10
D. 1/2

Solution

Probability of white = Number of white balls / Total balls = 4/10 = 2/5.

Correct Answer: C — 4/10

Q. A box contains 10 balls, of which 4 are white and 6 are black. If one ball is drawn at random, what is the probability that it is black?

A. 3/5
B. 2/5
C. 1/2
D. 6/10

Solution

Probability of drawing a black ball = Number of black balls / Total balls = 6/10 = 3/5.

Correct Answer: A — 3/5

Q. A box contains 10 light bulbs, of which 3 are defective. If one bulb is selected at random, what is the probability that it is not defective?

A. 3/10
B. 7/10
C. 1/2
D. 1/3

Solution

Total bulbs = 10, Non-defective bulbs = 10 - 3 = 7. Probability = Non-defective bulbs / Total bulbs = 7/10.

Correct Answer: B — 7/10

Q. A box contains 3 red balls and 2 blue balls. If one ball is drawn at random, what is the probability that it is red?

A. 1/5
B. 2/5
C. 3/5
D. 4/5

Solution

The total number of balls is 3 + 2 = 5. The number of red balls is 3. Therefore, the probability of drawing a red ball is 3/5.

Correct Answer: C — 3/5

Q. A box contains 3 red, 5 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue?

A. 1/10
B. 1/5
C. 1/2
D. 1/3

Solution

Total balls = 3 + 5 + 2 = 10. Probability of drawing a blue ball = Number of blue balls / Total balls = 5/10 = 1/2.

Correct Answer: B — 1/5

Q. A box contains 5 red balls and 3 blue balls. What is the probability of drawing a red ball? (2021)

A. 3/8
B. 5/8
C. 1/2
D. 1/3

Solution

Total balls = 5 + 3 = 8. Probability of red = 5/8.

Correct Answer: B — 5/8

Q. A class has 30 students with an average score of 75. If 5 new students join with an average score of 80, what is the new average? (2023)

A. 76
B. 77
C. 78
D. 79

Solution

Total score of 30 students = 30 * 75 = 2250. Total score of 5 new students = 5 * 80 = 400. New total = 2250 + 400 = 2650. New average = 2650 / 35 = 76.43.

Correct Answer: C — 78

Q. A class has 30 students with an average score of 75. If a new student joins and the average becomes 76, what is the score of the new student? (2023)

A. 80
B. 85
C. 90
D. 95

Solution

Total score of 30 students = 30 * 75 = 2250. New total = 31 * 76 = 2356. Score of new student = 2356 - 2250 = 106.

Correct Answer: B — 85

Q. A class has an average score of 75. If one student scored 90, what is the average score of the remaining students if there are 20 students in total?

A. 74
B. 75
C. 76
D. 77

Solution

The total score of the class is 75 * 20 = 1500. Removing the student who scored 90 gives a new total of 1500 - 90 = 1410. The average of the remaining 19 students is 1410 / 19 = 74.21, which rounds to 74.

Correct Answer: A — 74

Q. A class has the following scores in a test: 56, 78, 78, 82, 82, 82, 90, 91. What is the mode of the scores?

A. 56
B. 78
C. 82
D. 90

Solution

The mode is 82, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 82

Q. A class of 30 students has an average score of 75. If one student scores 90, what will be the new average? (2022)

A. 76
B. 77
C. 78
D. 79

Solution

Total score = 75 * 30 = 2250. New total = 2250 - 75 + 90 = 2265. New average = 2265 / 30 = 75.5.

Correct Answer: B — 77

Q. A class of students scored the following marks: 45, 50, 50, 55, 60, 60, 60, 70, 75. What is the mode of the scores?

A. 50
B. 55
C. 60
D. 70

Solution

The mode is 60, as it appears most frequently (3 times) in the data set.

Correct Answer: C — 60

Q. A class of students scored the following marks: 45, 55, 55, 60, 60, 60, 70, 75, 80. What is the mode of the scores?

A. 45
B. 55
C. 60
D. 70

Solution

The mode is 60, as it appears most frequently (3 times) in the scores.

Correct Answer: C — 60

Q. A class of students scored the following marks: 45, 55, 55, 60, 60, 60, 70, 75. What is the mode of the scores?

A. 45
B. 55
C. 60
D. 70

Solution

The mode is 60, as it appears most frequently (3 times) in the scores.

Correct Answer: C — 60

Q. A class of students scored the following marks: 45, 55, 55, 60, 70, 70, 70, 80, 90. What is the mode of the scores?

A. 55
B. 60
C. 70
D. 80

Solution

The mode is 70, as it appears most frequently (3 times) in the scores.

Correct Answer: C — 70

Q. A coin is tossed three times. What is the probability of getting at least one head?

A. 1/8
B. 1/2
C. 7/8
D. 3/8

Solution

Probability of getting no heads (all tails) = (1/2)^3 = 1/8. Therefore, probability of at least one head = 1 - 1/8 = 7/8.

Correct Answer: C — 7/8

Q. A data set has a mean of 20 and a variance of 16. What is the range of the data if the maximum value is 28? (2023)

A. 8
B. 12
C. 16
D. 20

Solution

If the variance is 16, the standard deviation is 4. The minimum value can be calculated as 20 - 4 = 16. Therefore, range = 28 - 16 = 12.

Correct Answer: B — 12

Q. A data set has a mean of 20 and a variance of 16. What is the range of the data if it is normally distributed? (2023)

A. 8
B. 16
C. 32
D. 64

Solution

In a normal distribution, approximately 95% of the data lies within 2 standard deviations from the mean. SD = √16 = 4. Range = 20 ± 2*4 = 20 ± 8 = 12 to 28.

Correct Answer: C — 32

Q. A data set has a mean of 50 and a variance of 25. What is the standard deviation? (2021)

A. 5
B. 10
C. 15
D. 20

Solution

Standard deviation is the square root of variance. Therefore, SD = √25 = 5.

Correct Answer: B — 10

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