10th Maths Unit 8 Important Questions | Statistics & Probability

Begin your final board countdown with the official 10th Maths First Revision Test 2026 Question Paper. This crucial revision test is a major milestone for SSLC students, specifically structured to evaluate your mastery over the core chapters under strict public exam conditions. This 2026 question paper features a comprehensive mix of foundational 2-mark problems, highly predicted 5-mark long answers, and vital 8-mark graph and geometry constructions aligned with the latest curriculum trends. Use this authentic test paper as a timed rehearsal to sharpen your problem-solving speed, perfect your step-by-step presentation, and lock in your path toward a perfect centum!

X-Maths UNIT - 8 Public Important Questions - 2026

1. A and B are two candidates seeking admission to IIT. The probability that A getting selected is 0.5 and the probability that both A and B getting selected is 0.3. Prove that the probability of B being selected is at most 0.8.

2. In a class of 50 students, 28 opted for NCC, 30 opted for NSS and 18 opted both NCC and NSS. One of the students is selected at random. Find the probability that (i) The student opted for NCC but not NSS. (ii) The student opted for NSS but not NCC. (iii) The student opted for exactly one of them.

3. In an apartment, in selecting a house from door numbers 1 to 100 randomly, find the probability of getting the door number of the house to be an even number or a perfect square number or a perfect cube number.

4. Two dice are rolled together. Find the probability of getting a doublet or sum of faces as 4.

5. A flower is selected at random from a basket containing 80 yellow, 70 red and 50 white flowers. Find the probability of selecting a yellow or red flower?

6. In a game, the entry fee is ₹150. The game consists of tossing a coin 3 times. Dhana bought a ticket for entry. If one or two heads show, she gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise she will lose. Find the probability that she (i) gets double entry fee (ii) just gets her entry fee (iii) loses the entry fee.

7. At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize. What is the probability that (i) the first player wins a prize (ii) the second player wins a prize, if the first has won?

8. A bag contains 12 blue balls and x red balls. If one ball is drawn at random (i) what is the probability that it will be a red ball? (ii) If 8 more red balls are put in the bag, and if the probability of drawing a red ball will be twice that of the probability in (i), then find x.

9. Write the sample space for tossing three coins using tree diagram.

10. Write the sample space for selecting two balls at a time from a bag containing 6 balls numbered 1 to 6 (using tree diagram).

11. A bag contains 6 green balls, some black and red balls. Number of black balls is as twice as the number of red balls. Probability of getting a green ball is thrice the probability of getting a red ball. Find (i) number of black balls (ii) total number of balls.

12. A bag contains 5 blue balls and 4 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is (i) blue (ii) not blue.

13. The standard deviation and mean of a data are 6.5 and 12.5 respectively. Find the coefficient of variation.

14. The standard deviation and coefficient of variation of a data are 1.2 and 25.6 respectively. Find the value of mean.

15. If the mean and coefficient of variation of a data are 15 and 48 respectively, then find the value of standard deviation.

16. The mean of a data is 25.6 and its coefficient of variation is 18.75. Find the standard deviation.

17. In a study about viral fever, the number of people affected in a town were noted as. Find its standard deviation:

Age in years	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Number of people affected	3	5	16	18	12	7	4

18. For a group of 100 candidates the mean and standard deviation of their marks were found to be 60 and 15 respectively. Later on it was found that the scores 45 and 72 were wrongly entered as 40 and 27. Find the correct mean and standard deviation.

19. The mean and variance of seven observations are 8 and 16 respectively. If five of these are 2, 4, 10, 12 and 14, then find the remaining two observations.

20. Find the variance and standard deviation of the wages of 9 workers given below: ₹310, ₹290, ₹320, ₹280, ₹300, ₹290, ₹320, ₹310, ₹280.

21. Find the range and coefficient of range of the following data:
(i) 63, 89, 98, 125, 79, 108, 117, 68
(ii) 43.5, 13.6, 18.9, 38.4, 61.4, 29.8

22. The mean and standard deviation of 15 observations are found to be 10 and 5 respectively. On rechecking it was found that one of the observation with value 8 was incorrect. Calculate the correct mean and standard deviation if the correct observation value was 23?

23. The marks scored by the students in a slip test are given below. Find the standard deviation of their marks:

x	4	6	8	10	12
f	7	3	5	9	5

24. 48 students were asked to write the total number of hours per week they spent on watching television. With this information find the standard deviation of hours spent for watching television:

x	6	7	8	9	10	11	12
f	3	6	9	13	8	5	4

25. Find the standard deviation of the following data 7, 4, 8, 10, 11. Add 3 to all the values then find the standard deviation for the new values.