Question

A number is selected from the numbers $2,3,3,5,5,5,7,7,7,7,9,9,9,9,9$ at random. Find the probability that the number selected is their median.

Answer 1

Finding the probability that the number selected is their median.

The given data is $2,3,3,5,5,5,7,7,7,7,9,9,9,9,9$

Step 1:- Finding the median of the given data.

Total number of terms $\left(n\right)$$=15$

Median$={\left(\frac{n+1}{2}\right)}^{th}$term

So, median$={\left(\frac{15+1}{2}\right)}^{th}$term

$={\left(\frac{16}{2}\right)}^{th}$

$=8^{th}$ term $i.e7$

Step 2:- Finding the required probability

Let $\text{P}\left(\text{E}\right)$ be the probability that the number selected is their median.

All possible outcomes$=$$2,3,3,5,5,5,7,7,7,7,9,9,9,9,9$

$\therefore$Number of possible outcomes$=15$

Outcomes having $7$$\left(median\right)$$=7,7,7,7$

$\therefore$Number of favourable outcomes$=4$

We know that $\text{P}\left(\text{E}\right)\text{=}\frac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}$

So, $\text{P}\left(\text{E}\right)$$=\frac{4}{15}$

Hence, probability that the number selected is their median$=\frac{\mathbf{4}}{\mathbf{15}}$