Question

A die is 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

(i) Total no of possible outcomes = 6 {1, 2, 3, 4, 5, 6}

E ⟶ Event of getting a prime no.

No. of favorable outcomes = 3 {2, 3, 5}

P(E) = (No. of favorable outcomes)/(Total no. of possible outcomes)

P(E) = 3/6 = 1/2

(ii) E ⟶ Event of getting 2 or 4.

No. of favorable outcomes = 2 {2, 4}

Total no. of possible outcomes = 6

Then, P(E) = 2/6 = 1/3

(iii) E ⟶ Event of getting a multiple of 2 or 3

No. of favorable outcomes = 4 {2, 3, 4, 6}

Total no. of possible outcomes = 6

Then, P(E) = 4/6 = 2/3

(iv) E ⟶ Event of getting an even prime no.

No. of favorable outcomes = 1 {2}

Total no. of possible outcomes = 6 {1, 2, 3, 4, 5, 6}

P(E) = 1/6

(v) E ⟶ Event of getting a no. greater than 5.

No. of favorable outcomes = 1 {6}

Total no. of possible outcomes = 6

P(E) = 1/6

(vi) E ⟶ Event of getting a no. lying between 2 and 6.

No. of favorable outcomes = 3 {3, 4, 5}

Total no. of possible outcomes = 6

P(E) = 3/6 = 1/2