Question

If a number of two digits is formed with the digits $2,3,5,7,9$ without repetition of digits.

The probability that the number formed is $35,$ is

• A. $\frac{1}{10}$
• B. $\frac{1}{20}$
• C. $\frac{1}{30}$
• D. none of these

Answer 1

The correct option is B

$\frac{1}{20}$

Finding the probability:

Let the sample space is $\mathrm{S}$, that a number of two digits formed with the digits $2,3,5,7,9$ without the repetition of digits.

$\Rightarrow$$\mathrm{S}=\left\{23,25,27,29,32,35,37,39,52,53,57,59,72,73,75,79,92,93,95,97\right\}$

Total outcome is $\left\{23,25,27,29,32,35,37,39,52,53,57,59,72,73,75,79,92,93,95,97\right\}=20$

Favorable outcome, the event that the number formed $35$ is $1$.

Now, the required probability is $\frac{\mathbf{F}\mathbf{a}\mathbf{v}\mathbf{o}\mathbf{r}\mathbf{a}\mathbf{b}\mathbf{l}\mathbf{e}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}=\frac{1}{20}$

Hence, correct answer is option $\left(B\right)$.