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.

Solution:

The sample space of the given experiment is given by

S = {1, 2, 3, 4, 5, 6}; n (S) = 6

(i) Let A be the event of the occurrence of a prime

Accordingly, A = {2, 3, 5}; n (A) = 3

P (A) = Number of outcomes favourable to A/Total number of possible outcomes.

Therefore, the required probability is,

P (A) = n (A)/n (S)

= 3/6

= 1/2

(ii) Let B be the event of the occurrence of a number greater than or equal to 3.

Accordingly, B = {3, 4, 5, 6}; n ( B) = 4

P (B) = Number of outcomes favourable to B/Total number of possible outcomes.

Therefore,

P (B) = n (B)/n (S)

= 4/6

= 2/3

(iii) Let C be the event of the occurrence of a number less than or equal to 1.

Accordingly, C = {1}; n (C) = 1

P (C) = Number of outcomes favourable to C/Total number of possible outcomes.

Therefore,

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

= 1/6

(iv) Let D be the event of the occurrence of a number greater than 6 .

Accordingly, D = Φ; n ( D) = 0

P (D) = Number of outcomes favourable to D/Total number of possible outcomes.

Therefore,

P (D) = n (D)/n (S)

= 0/6

= 0

(v) Let E be the event of the occurrence of a number less than 6.

Accordingly, E = {1, 2, 3, 4, 5}; n (E) = 5

P (E) = Number of outcomes favourable to E/Total number of possible outcomes.

Therefore,

P (E) = n (E)/n (S)

= 5/6

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NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.3 Question 3

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.

Summary:

When a die is thrown, the probability of the given events are: (i) 1/2 (ii) 2/3 (iii) 1/6 (iv) 0 (v) 5/6