In a single throw of a die, find the probability?

In a single throw of a die, find the probability of getting:
(i) an odd number
(ii) a number less than 5
(iii) a number greater than 5
(iv) a prime number
(v) a number less than 8
(vi) a number divisible by 3
(vii) a number between 3 and 6
(viii) a number divisible by 2 or 3.

Solution:

A die is thrown and on its faces, numbers 1 to 6 are written.
Total numbers of possible outcomes = 6
(i) Probability of an odd number,
odd number are 1, 3 and 5
P(E) = $\frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }$
= $\\ \frac { 3 }{ 6 }$
= $\\ \frac { 1 }{ 2 }$
(ii) A number less them 5 are 1, 2, 3, 4
Probability of a number less than 5 is
P(E) = $\frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }$
= $\\ \frac { 4 }{ 6 }$
= $\\ \frac { 2 }{ 3 }$
(iii) A number greater than 5 is 6
Probability of a number greater than 5 is
P(E) = $\frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }$
= $\\ \frac { 1 }{ 6 }$
(iv) Prime number is 2, 3, 5
Probability of a prime number is
P(E) = $\frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }$
= $\\ \frac { 3 }{ 6 }$
= $\\ \frac { 1 }{ 2 }$
(v) Number less than 8 is nil
P (E) = 0
(vi) A number divisible by 3 is 3, 6
Probability of a number divisible by 3 is
P(E) = $\frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }$
= $\\ \frac { 2 }{ 6 }$
= $\\ \frac { 1 }{ 3 }$
(vii) Numbers between 3 and 6 is 4, 5
Probability of a number between 3 and 6 is
P(E) = $\frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }$
= $\\ \frac { 2 }{ 6 }$
= $\\ \frac { 1 }{ 3 }$
(viii) Numbers divisible by 2 or 3 are 2, 4 or 3,
Probability of a number between 2 or 3 is
P(E) = $\frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }$
= $\\ \frac { 2 }{ 6 }$
= $\\ \frac { 1 }{ 3 }$