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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
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
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