# SCERT Kerala Mathematics Textbook Solutions/ Mathematics of Chance.

**Mathematics of Chance / Chapter 3 SCERT Kerala Mathematics is about the textbook solutions of Class 10 Mathematics. Here you can find out practice problems from the Chapter Mathematics of Chance.**

**SCERT Kerala Class 10 Mathematics Textbook SolutionsMathematics of Chance – Chapter 3Possibilities as numbers:Answer the following:**

- A box contains 6 black and 4 white balls. If a ball is taken from it, what is the probability of it being black? And the probability of it being white?

Solution:

Number of black balls = 6

Number of white balls = 4

Total number of balls = 10

Probability of being black = 6/10 = 3/5

Probability of being white = 4/10 = 2/5 - There are 3 red balls and 7 green balls in a bag, 8 red and 7 green balls in another.

i) What is the probability of getting a red ball from the first bag?

ii) From the second bag?

iii) If all the balls are put in a single bag, what is the probability of getting a red ball from it?

Solution:

i) Number of red balls in the first bag = 3

Number of green balls in the first bag = 7

Total number of balls = 10

Probability of getting a red ball from the first bag = 3/10

ii) Number of red balls in the second bag = 8

Number of green balls in the second bag = 7

Total number of balls = 15

Probability of getting a red ball from the second bag = 8/15

iii) If all the bags are put in a single bag, number of red balls = 3 + 8 = 11

Number of green balls = 7 + 7 = 14

Total number of balls = 11 + 14 = 25

Probability of getting a red ball = 11/25 - One is asked to say a two-digit number. What is the probability of it being a perfect square?

Solution:

Two-digit perfect squares are 16, 25, 36, 49, 64, 81.

So there are 6 perfect squares.

Total numbers of two-digit numbers are 90.

Therefore, Probability of being a perfect square = 6/90 = 1/15 - Numbers from 1 to 50 are written on slips of paper and put in a box. A slip is to be drawn from it: but before doing so, one must make a guess about the number: either prime number or a multiple of five. Which is the better guess? Why?

Solution:

Prime numbers from 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

There are 15 prime numbers from 1 to 50.

Probability of getting a prime number = 15/50 = 3/10

The numbers from 1 to 50 which are multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

There are 10 multiples of 5 in between 1 and 50.

Probability of getting a multiple of 5 = 10/50 = 1/5

Since 3/10 > 1/5, Probability of getting prime numbers is the better guess. - A bag contains 3 red beads and 7 green beads. Another contains one red and one green more. The probability of getting a red from which bag is more?

Solution:

Number of red beads in the first bag = 3

Number of green beads in the first bag = 7

Total number of beads = 10

Probability of getting a red bead from first bag = 3/10

Number of red beads in the second bag = 3 + 1 = 4

Number of green beads in the second bag = 7 + 1 = 8

Total number of beads = 4 + 8 = 12

Probability of getting a red bead from the second bag = 4/12 = 1/3

Since 1/3 > 3/10, the probability of getting a red bead from the second bag is more.