# SCERT Kerala Class 10 Mathematics/ Mathematics of Chance.

SCERT Kerala Class 10 Mathematics / Mathematics of Chance is about the questions based on Probability. Here you can find out practice problems and model questions for Class 10 Mathematics.

SCERT Kerala Class 10 Mathematics/ Mathematics of Chance – Chapter 3
Extra Questions for Practice/ Model Questions.

1. A pack of cards contains the numbers marked 1, 2, 3 ….10. A card is drawn at random. What is the probability that the number on the card is a
a) Prime number
b) Composite number
c) Perfect square

Solution:
Total numbers are 10.
a) Prime numbers below 10 are 2, 3, 5 and 7.
Number of favourable cases are 4.
Probability (getting a prime number) = 4/10 = 2/5
b) Composite numbers are 4, 6, 8, 9 and 10.
Number of favourable cases are 5.
Probability (getting a composite number) = 5/10 = ½
c) Perfect squares below 10 are 1, 4 and 9.
Number of favourable cases are 3.
Probability (getting a perfect square) = 3/10
2. A box contains numbers from 1 to 20.A slip is to be drawn it.
a) Find the probability of getting an odd number?
b) Find the probability of getting an even number?
c) Find the probability of getting a prime number?

Solution:
a) Odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17,19
Total 10 prime numbers are there in between 1 and 20.
So probability (getting an odd number) = 10/20 = ½
b) Even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
Total 10 even numbers are there in between 1 and 20.
Probability (getting an even number) = 10/20 = ½
c) Prime numbers are 2, 3, 5, 7, 11, 13, 17 and 19.
Total 8 prime numbers are there in between 1 and 20
Probability (getting a prime number) = 8/20 = 4/10= 2/5.
3. A box contains 15 red balls and 10 white balls. Take one ball from this.
a) What is the probability of getting a red ball?
b) What is the probability of getting a white ball?

Solution:
Total number of balls = 25
a) Probability (getting a red ball) = 15/25 = 3/5
b) Probability (getting a white ball) = 10/25 = 2/5
4. Two dice are tossed together. From the number of pairs
a) Find the probability of getting both odd?
b) Find the probability of getting both even?
c) Find the probability of getting both being same?

Solution:
When two dice are tossed together, we will get 36 pairs.
a) Pairs with both numbers are odd = (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5)(5, 1), (5, 3), (5, 5)
There are 9 such pairs where both are odd numbers.
Probability (getting both odd) = 9/36 = ¼
b) Pairs with both numbers are even = (2, 2), (2, 4), (2, 6), (4, 2), (4, 4), (4, 6) ,(6, 2), (6, 4), (6, 6)
There are 9 such pairs where both are even numbers.
Probability (getting both are even) = 9/36 = ¼
c) Pairs with both numbers are same = (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
There are 6 such pairs.
Probability (getting both being same) = 6/36 = 1/6
5. Consider all 2 digit numbers.
a) Find the probability of both digits being the same?
b) Find the probability of getting a perfect square?

Solution:
Total number of two digit numbers = 90
a) The numbers where both digits same = 11, 22, 33, 44, 55, 66, 77, 88, 99
There are 9 such numbers.
Probability (both digits being the same) = 9/90 = 1/10
b) Perfect squares are 16, 25, 36, 49, 64 and 81.
There are 6 two digit perfect squares.
Probability (getting a perfect square) = 6/90 = 3/45 = 1/15.