A die is thrown once. What is the probability

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A die is thrown once. What is the probability that the
(i) The number is even
(ii) number is greater than 2?

Solution:

Dice is thrown once
Sample space = {1, 2, 3, 4, 5, 6}
(i) No. of ways in favour = 3
(∵ Even numbers are 2, 4, 6)
Total ways = 6
Probability = \\ \frac { 3 }{ 6 } = \\ \frac { 1 }{ 2 }
(ii) No. of ways in favour = 4
(Numbers greater than 2 are 3, 4, 5, 6)
Total ways = 6
Probability = \\ \frac { 4 }{ 6 } = \\ \frac { 2 }{ 2 }

A die has 6 faces marked by the given numbers as shown below:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 22 Probability Ex 22 Q18.1
The die is thrown once. What is the probability of getting
(i) a positive integer.
(ii) an integer greater than – 3.
(iii) the smallest integer?

Solution:

Total outcomes n(S)= 6
(i) a positive integer = (1, 2, 3)
No. of favourables n(E) = 3
Probability = \\ \frac { n(E) }{ n(S) }
= \\ \frac { 3 }{ 6 }
= \\ \frac { 1 }{ 2 }
(ii) Integer greater than -3
= (1, 2, 3, -1, -2)
No. of favourables n(E) = 5
Probability = \\ \frac { n(E) }{ n(S) }
= \\ \frac { 5 }{ 6 }
(iii) Smallest integer = -3
No. of favourables n(E) = 1
Probability = \\ \frac { n(E) }{ n(S) }
= \\ \frac { 1 }{ 6 }

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