# 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 3Extra Questions for Practice/ Model Questions.Answer the following:**

**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**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.**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**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**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.