10th Maths Chapter 8 Important 5 Mark Questions with Answers

Secure your high scores in the long-answer section with this curated collection of 10th Maths Chapter 8 Important 5 Mark Questions. Statistics and Probability is one of the most scoring chapters in the syllabus, frequently featuring highly predictable 5-mark problems in the public exam. This guide focuses on the most critical textbook examples and exercise problems—ranging from calculating standard deviation and coefficient of variation to solving complex addition theorems of probability. Practice these high-yield problems to perfect your step-by-step working, master the calculation methods, and ensure you secure full marks in Section-C!

IMPORTANT FIVE MARKS:

10th STANDARD

CHAPTER-8 (PROBABILITY)

1. 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

2. 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.

3. A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the numbers 1, 2, 3, ... 12. What is the probability that it will point to (i) 7 (ii) a prime number (iii) a composite number?

4. 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?

5. 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.

6. 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

7. Three fair coins are tossed together. Find the probability of getting (i) all heads (ii) atleast one tail (iii) atmost one head (iv) atmost two tails

8. Two customers Priya and Amuthan are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another day. What is the probability that both will visit the shop on (i) the same day (ii) different days (iii) consecutive days?

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

10. 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

11. 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.

12. Two dice are rolled once. Find the probability of getting an even number on the first die or a total of face sum 8.

13. A box contains cards numbered 3, 5, 7, 9, ... 35, 37. A card is drawn at random from the box. Find the probability that the drawn card have either multiples of 7 or a prime number.

14. Three unbiased coins are tossed once. Find the probability of getting atmost 2 tails or atleast 2 heads.

15. A coin is tossed thrice. Find the probability of getting exactly two heads or atleast one tail or two consecutive heads.

16. In a town of 8000 people, 1300 are over 50 years and 3000 are females. It is known that 30% of the females are over 50 years. What is the probability that a chosen individual from the town is either a female or over 50 years?

17. In a class of 35, students are numbered from 1 to 35. The ratio of boys to girls is 4:3. The roll numbers of students begin with boys and end with girls. Find the probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number.