Question

One is asked to say a natural number less than 10. (a) What is the probability of it being an odd number?
(b) What is the probability that it will not be an even number?

Answer 1

Step-by-step explanation:

If there are first 10 natural numbers, what is the probability of getting an even number and what is the probability of a prime number among them?

Sample space :

1,2,3,4,5,6,7,8,9,10

Total number of observations=10

(a) probability of even number

Favourable numbers are 2,4,6,8,10

thus there are 5 favourable events

Hence probability of even number

=5/10

=1/2 or 0.5

(b) prime number

2,3,5,7 are prime numbers from 1–10

Thus there are 4 favorable numbers.

Probability=4/10

=2/5 or 0.4

Answer 2

Given: One is asked to say a natural number less than 10.

To find:

(a) The probability of it being an odd number.

(b) The probability that it will not be an even number.

Solution:

• Probability of an event is a measure of the chances for its occurrence.
• It is calculated by dividing the number of favourable outcomes by the number of total possible outcomes.

(a)

• There are 5 odd numbers that are less than 10, so the number of favourable outcomes is 5.
• There are 9 natural numbers that are less than 10, so the number of total possible outcomes is 9.
• The probability is given by,

        $P(E) = \frac{5}{9}$

(b)

• The probability that it will not be an even number, is the same as the probability of getting an odd number.
• So, this probability is also given by,

        $P(E) = \frac{5}{9}$

Therefore, the probability of it

(a) being an odd number is 5/9.

(b) not being an even number is 5/9.