Question

In a bowl there are $15$ first natural numbers. John chooses a number randomly $15$ times with replacement. All the outcomes are listed in the table below.

Outcomes	1	2	4	6	7	8	10	11	13	15
Number of times occurs	I	II	I	I	I	I	III	I	I	III

What is the experimental probability of choosing an even number?

• A. $\frac{7}{15}$
• B. $\frac{8}{15}$
• C. $\frac{9}{15}$
• D. None of the above

Answer 1

The correct option is B $\frac{8}{15}$

John picks a number $15$ times from the bowl with replacement. The outcomes from these $15$ picks are summarized in the below experimental table.

Outcomes	1	2	4	6	7	8	10	11	13	15
Number of times occurs	I	II	I	I	I	I	III	I	I	III

The above table signifies that John picks $1$ one time, $2$ two times and so on out of his $15$ picks.

Total number of times John picks numbers= $15$
Number of times John picks an even numbers $(2,4,6,8,10)$= $\text{II+I+I+I+III}=8$
[As the even munbers $2,4,6,8\text{and}10$ $\text{occur II, I, I, I and III times, respectively}$]

$\therefore \text{P(picking an even number)}=\frac{\text{Number of picks for even numbers}}{\text{Total number of picks}}$,
where $\text{P}$ = Experimental probability of choosing even number

$\Rightarrow \text{P}=\frac{8}{15}$

$\therefore$ The experimental probability of choosing an even number is $\frac{8}{15}$.