Question

A box contains $15$ tickets numbered $1,2,...,15$. Seven tickets are drawn at random one after the other with replacement. The probability that the greatest number on a drawn ticket is $9$ is

• A. ${\left(\frac{9}{10}\right)}^6$
• B. ${\left(\frac{8}{15}\right)}^7$
• C. ${\left(\frac{3}{5}\right)}^7$
• D. None of these

Answer 1

The correct option is C

${\left(\frac{3}{5}\right)}^7$

An explanation for the correct option.

Step 1: Find the possible outcomes for a given experiment and an event.

We have been given that, a box contains $15$ tickets numbered $1,2,...,15$. Seven tickets are drawn at random one after the other with replacement.

We need to find the probability that the greatest number on a drawn ticket is $9$

For a given experiment the number of possible outcomes would be,

$n\left(S\right)={15}^7$

Let event $A:$the greatest number on a drawn ticket is $9$

Since, the greatest number on the drawn ticket is $9$, so, it can be $1,2,3,...,9$ and seven tickets are drawn at random one after the other with replacement.

$\Rightarrow n\left(A\right)=9^7$

Step 2: Find the required probability.

Using the formula of probability, the probability that the greatest number on a drawn ticket is $9$ would be,

$$\begin{gathered} \Rightarrow P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)} \\ \Rightarrow P\left(A\right)=\frac{9^7}{{15}^7} \\ \Rightarrow P\left(A\right)={\left(\frac{9}{15}\right)}^7 \\ \Rightarrow P\left(A\right)={\left(\frac{3}{5}\right)}^7 \end{gathered}$$

Therefore, option (C) is the correct answer.