# 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 Solutions
Mathematics of Chance – Chapter 3
Possibilities as numbers:

1. 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
2. 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
3. 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
4. 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.
5. 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.