**Question:**

A die is thrown, Find the probability of getting:

(a) a prime number

(b) 2 or 4

(c) a multiple of 2 or 3

(d) an even prime number

(e) a number greater than 5

(f) a number lying between 2 and 6

**Solution:**

GIVEN: A dice is thrown once

TO FIND

(i) Probability of getting a prime number

(ii) Probability of getting 2 or 4

(iii) Probability of getting a multiple of 2 or 3.

(iv) Probability of getting an even number

(v) Probability of getting a number greater than five.

(vi) Probability of lying between 2 and 6

Total number on a dice is 6.

(i) Prime number on a dice are 2,3,5

Total number of prime numbers on dice is 3

We know that PROBABILITY =

Hence probability of getting a prime number =

(ii) for getting 2 and 4 favorable outcome are 2

We know that PROBABILITY =

Hence probability of getting 2 or 4 =

(iii) Multiple of 2 are 3 are 2, 3, 4 and 6

Hence favorable outcome is 4

We know that PROBABILITY =

Hence probability of getting an multiple of 2 or 3 =

(iv) an even prime number is 2

Hence favorable outcome is 1

We know that PROBABILITY =

Hence probability of getting an even prime number

(v) A number greater than 5 is 6

Hence favorable outcome is 1

We know that PROBABILITY =

Hence probability of getting a number greater than 5

(vi) Total number on a dice is 6.

Number lying between 2 and 6 are 3, 4 and 5

Total number of number lying between 2 and 6 is 3

We know that PROBABILITY =

Hence probability of getting a number lying between 2 and 6 =