1.

A die is thrown, find the probability of following events: (i) A prime number will appear, (ii) A number greater than or equal to 3 will appear, (iii) A number less than or equal to one will appear, (iv) A number more than 6 will appear, (v) A number less than 6 will appear.

Answer»

Required sample space associated with an experiment is S = {1, 2, 3,4, 5, 6} 

∴ n(S) = 6 

(i) Let A : ‘a prime number will appear’ 

⇒ A = {2,3,5} ∴ n(A) = 3 

∴ Required Probability

P(A) = n(A)/n(S) = 3/6 = 1/2

(ii) Let B: ‘a number ≥ 3 will appear’ 

⇒ B = {3,4,5,6} ∴ n(B) = 4 

∴ Required Probability

P(B) = n(B)/n(S) = 4/6 = 2/3

(iii) Let C: ‘a number ≤ 1 will appear’ 

⇒ C = (1) 

∴ Required Probability

P(C) = n(C)/n(S) = 1/6

(iv) Let D: ‘a number >6 will apper’ ⇒ D = { } = ϕ

= P(D) = 0/6 = 0

(v) E : ‘ a number < 6 will appear’ 

⇒ E= {1, 2, 3, 4, 5} ∴ n(E) = 5 

∴ Required probability


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