SAMACHEER KALVI CLASS 10 STATISTICS AND PROBABILITY

 SAMACHEER KALVI CLASS 10

STATISTICS AND PROBABILITY

IMPORTANT CONCEPT BASED QUESTIONS

TOTAL NUMBER OF QUESTIONS: 30

1.  Find the range and coefficient of range of the following data.

(i) 63, 89, 98, 125, 79, 108, 117, 68

2. Find the variance and standard deviation of the wages of 9 workers given below:

₹ 310, ₹ 290, ₹ 320, ₹ 280, ₹ 300, ₹ 290, ₹ 320, ₹ 310, ₹ 280.

3. If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value.

4. Find the standard deviation of the first 21 natural numbers.

5. If the standard deviation of a data is 3.6 and each value of the data is divided by 3, then find the new variance and new standard deviation.

6. The rainfall recorded in various places of five districts in a week are given below.

Find its standard deviation.

7. The measurements of the diameters (in cms) of the plates prepared in a factory are given below. Find the standard deviation.


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

9. If n = 5, x¯ = 6, Σx2 = 765, then calculate the coefficient of variation.

10. Find the coefficient of variation of 24, 26, 33, 37, 29, 31.

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

12. The total marks scored by two students Sathya and Vidhya in 5 subjects are 460 and 480 with standard deviation of 4.6 and 2.4 respectively. Who is more consistent in performance?

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

14. A coin is tossed thrice. What is the probability of getting two consecutive tails?

15. 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

16. 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

17. A bag contains 5 red balls, 6 white balls, 7 green balls, 8 black balls. One ball is drawn at random from the bag. Find the probability that the ball drawn is
(i) white
(ii) black or red
(iii) not white
(iv) neither white nor black

18. 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?

19. If P (A) = 23, P(B) = 25, P(A ∪ B) = 13, then find P(A ∩ B).

20. If A and B are two mutually exclusive events of a random experiment and P (not A) = 0.45, P (A ∪ B) = 0.65, then find P(B).

21. The probability that atleast one of A and B occur is 0.6. If A and B occur simultaneously with probability 0.2, then find P(A¯¯¯¯) + P(B¯¯¯¯).


22. The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then find the probability of neither A nor B happen.

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

24. A and B are two events such that, P(A) = 0.42, P(B) = 0.48, and P(A∩B)=016. Find (i) P(not A)

(ii) P(not B)
(iii) P(A or B)

25. The probability that a person will get an electrification contract is 35 and the probability that he will not get plumbing contract is 58. The probability of getting atleast one contract is 57. What is the probability that he will get both?

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

27. 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.

28. From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability of its being either a red king or a black queen.

29. 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) = 16, P(B ∩ C) = 14, P(A ∩ C) = 18, P(A ∪ B ∪ C) = 910 and P (A ∩ B ∩ C) = 115, then find P(A), P(B) and P(C)?

30. In a class of 35, students are numbered from 1 to 35. The ratio of boys and 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.