Question

A die thrown. Find the probability of getting :

(i) a prime number

(ii) 2 or 4

(iii) a multiple of 2 or 3

(iv) an even prime number

(v) a number greater than 5

(vi) a number lying between 2 and 6

Answer 1

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 =$\frac{Numberoffavorableevent}{Totalnumberofevent}$

Hence, probability of getting a prime number = $\frac{3}{6}$ = $\frac{1}{2}$

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

We know that;

Probability =$\frac{Numberoffavorableevent}{Totalnumberofevent}$

Hence probability of getting 2 or 4 = $\frac{2}{6}$ = $\frac{1}{3}$

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

Hence favorable outcome is 4

We know that;

Probability = $\frac{Numberoffavorableevent}{Totalnumberofevent}$

Hence, probability of getting an multiple of 2 or 3 = $\frac{4}{6}$ = $\frac{2}{3}$

(iv) An even prime number is 2

So, favorable outcome is 1

We know that,

Probability = $\frac{Numberoffavorableevent}{Totalnumberofevent}$

Hence, probability of getting an even prime number = $\frac{1}{6}$

(v) A number greater than 5 is 6

So, favorable outcome is 1

We know that;

Probability = $\frac{Numberoffavorableevent}{Totalnumberofevent}$

Hence probability of getting a number greater than 5 = $\frac{1}{6}$

(vi) Total number on a dice is 6.

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

Total number of number lying between 2 and 6 is 3

We know that;

Probability = $\frac{Numberoffavorableevent}{Totalnumberofevent}$

Hence, probability of getting a number lying between 2 and 6 = $\frac{3}{6}$ = $\frac{1}{2}$