Question

A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability that the number formed is
(1) an odd number ?
(2) a multiple of 5 ?

Answer 1

Sample Space (S) = {23, 25, 27, 29, 32, 35, 37, 39, 52, 53, 57, 59, 72, 73, 75, 79, 92, 93, 95, 97}
∴ n(S) = 20

(1) Event A: the number is odd
A = {23, 25, 27, 29, 35, 37, 39, 53, 57, 59, 73, 75, 79, 93, 95, 97}
∴ n(A) = 16
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{\mathrm{n}\left(\mathrm{A}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{16}{20} \\ =\frac{4}{5} \end{gathered}$$
Hence, the probability that the number is odd is $\frac{1}{6}$.
(2) Event B: the number is a multiple of 5
B = {25, 35, 75, 95}
∴ n(B) = 4
$$\begin{gathered} \therefore \mathrm{P}\left(\mathrm{B}\right)=\frac{\mathrm{n}\left(\mathrm{B}\right)}{\mathrm{n}\left(\mathrm{S}\right)} \\ =\frac{4}{20} \\ =\frac{1}{5} \end{gathered}$$
​Hence, the probability that the number is a multiple of 5 is $\frac{1}{5}$.