Question

A die is thrown once. Find the probability of getting
i) a Prime Number ii) a number lying between 2 and 6
iii) an odd number iv) multiple of 3

Answer 1

Step-by-step explanation:

Given:-

A die is thrown once

To find:-

Find the probability of getting

i) a Prime Number ii) a number lying between 2 and 6 iii) an odd number iv) multiple of 3

Solution:-

We know that

A die is thrown'n' times then the total possible outcomes = 6^n

Given that

A die is thrown once then the total number of possible outcomes = 6^1 = 6

They are 1,2,3,4,5,6

Sample space = {1,2,3,4,5,6}

i) Probability of getting a prime number :-

The prime numbers = 2,3,4

Number of favourable outcomes = 3

we know that

Probability of an event= Number of favourable outcomes/ Total number of all possible outcomes

Probability of getting a prime number

= 3/6

=1/2

Probability of getting a prime number = 1/2

ii)Probability of getting a number lying between 2 and 6:-

The numbers lying between 2 and 6 =3,4,5

Number of favourable outcomes = 3

we know that

Probability of an event= Number of favourable outcomes/ Total number of all possible outcomes

Probability of getting a number lying between 2 and 6

= 3/6

=1/2

Probability of getting a number lying between 2 and 6 = 1/2

iii) Probability of getting an odd number:-

Odd numbers = 1,3,5

Number of favourable outcomes = 3

we know that

Probability of an event= Number of favourable outcomes/ Total number of all possible outcomes

Probability of getting an odd number

= 3/6

=1/2

Probability of getting an odd number = 1/2

iv) Probability of getting a multiple of 3:-

Multiples of 3 = 3,6

Number of favourable outcomes = 2

we know that

Probability of an event= Number of favourable outcomes/ Total number of all possible outcomes

Probability of getting multiple of 3

= 2/6

=1/3

Probability of getting a multiple of 3 = 1/3

Answer:-

i)Probability of getting a prime number = 1/2

ii)Probability of getting a number lying between 2 and 6 = 1/2

iii)Probability of getting an odd number = 1/2

iv)Probability of getting a multiple of 3 = 1/3

Used formulae:-

1.A die is thrown'n' times then the total possible outcomes = 6^n

2.Probability of an event= Number of favourable outcomes/ Total number of all possible outcomes