10th Maths Unit 8 Important 5 Mark Questions

Seal your victory in the final chapter of your syllabus by practicing the 10th Maths Unit 8 Important 5 Marks questions. Statistics and Probability is a highly scoring, concept-heavy unit that guarantees essential long-answer questions in the board exam. This chapter regularly features 5-mark problems on calculating the standard deviation and variance of ungrouped and grouped data, finding the coefficient of variation (C.V.), and solving complex probability problems involving coins, dice, cards, and leap years. This expert-curated list compiles the most repeated questions and expected compulsory problems, giving you the structured formulas and step-by-step methods needed to achieve a perfect score.

UNIT - 8 (STATISTICS & PROBABILITY)

IMPORTANT 5 MARKS QUESTIONS

1. Find the mean and variance of the first n natural numbers.

2. 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

3. The following table gives the values of mean and variance of heights and weights of the 10th standard students of a school:

	HEIGHT	WEIGHT
MEAN	155 cm	46.50 kg
VARIANCE	72.25 cm	28.09 kg

Which is more varying than the other?

4. If n = 5, x̄ = 6, Σx² = 765, then calculate the coefficient of variation.

5. A bag contains 6 green balls, some black and red balls. Number of black balls is twice 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.

6. Two dice are rolled. Find the probability that the sum of outcomes is (i) equal to 4 (ii) greater than 10 (iii) less than 13.

7. 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.

8. Two unbiased dice are rolled once. Find the probability of getting:
(i) a doublet (equal numbers on both dice)
(ii) the product as a prime number
(iii) the sum as a prime number
(iv) the sum as 1

9. Three fair coins are tossed together. Find the probability of getting:
(i) all heads
(ii) at least one tail
(iii) at most one head
(iv) at most two tails

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

11. 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.

12. 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.

13. Three unbiased coins are tossed once. Find the probability of getting at most 2 tails or at least 2 heads.

14. A coin is tossed thrice. Find the probability of getting exactly two heads or at least one tail or two consecutive heads.

15. If A, B, C are any three events such that probability of B is twice as that of probability of A and probability of C is thrice as that of probability of A and if P(A ∩ B) = ¹/₆, P(B ∩ C) = ¹/₄, P(A ∩ C) = ¹/₈, P(A ∪ B ∪ C) = ⁹/₁₀, P(A ∩ B ∩ C) = ¹/₁₅ then find P(A), P(B), and P(C)?