Question

A die is thrown then find the probability of getting
(i) an odd number.
(ii) a perfect square.
(iii) a number greater than 3.

Answer 1

Given:
A die is thrown.
The sample space is {1, 2, 3, 4, 5, 6}.
Or,
n(S) = 6

(i) Let A be the event of getting an odd number.
We have:
A = {1, 3, 5}
∴ n(A) = 3
Thus, we get:
P(A) =$\frac{n\left(\mathrm{A}\right)}{n\left(\mathrm{S}\right)}$
$\Rightarrow$P(A) =$\frac{3}{6}=\frac{1}{2}$

(ii) Let B be the event of getting a number that is a perfect square.
We have:
B = {1, 4}
∴ n(B) = 2
Thus, we get:
P(B) =$\frac{n\left(\mathrm{B}\right)}{n\left(\mathrm{S}\right)}$
$\Rightarrow$ P(B) =$\frac{2}{6}=\frac{1}{3}$

(iii) Let C be the event of getting a number greater than three.
We have:
C = {4, 5, 6}
∴ n(C) = 3
Thus, we get:
P(C) = $\frac{n\left(\mathrm{C}\right)}{n\left(\mathrm{S}\right)}$
$\Rightarrow$P(C) =$\frac{3}{6}=\frac{1}{2}$