Question

An office receives a shipment of identical boxes containing office supplies. The shipment contains 6 boxes of pencils, 14 boxes of pens, and 16 boxes of paper. How many additional boxes of paper must be added to the original 36 boxes in order for the probability of randomly selecting a box of paper from this shipment to be exactly 1/2 ?

Answer 1

Answer:

4

Step-by-step explanation:

Given that:

There are 6 boxes of pencils, 14 boxes of pens and 16 boxes of paper.

Total number of original boxes = 6 + 14 + 16 = 36

To find:

Number of additional boxes of paper to be added so that the probability of getting a paper box while selecting a random box becomes exactly $\frac{1}{2}$.

Solution:

First of all, let us have a look at the formula of probability:

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Here, number of favorable cases will be equal to the number of paper boxes and

Total number of cases will be equal to the total number of boxes available.

Let us first calculate the original probability:

$\frac{16}{36}\neq \frac{1}2$

If 1 paper box is added, then probability

$\frac{17}{37}\neq \frac{1}2$

If 2 paper boxes are added, then probability

$\frac{18}{38}\neq \frac{1}2$

If 3 paper boxes is added, then probability

$\frac{19}{39} \neq \frac{1}2$

If 4 paper boxes is added, then probability

$\frac{20}{40} = \frac{1}2$

Therefore, we need to add 4 paper boxes.