Question

A student reaches into a bag that contains 14 blue pens, 8 black pens, and 6 redpens. What is the probability that the students will pick NOT a blue or black pen?Your answer can be as a fraction (simplify) or percent rounded to the nearest wholepercent

Answer 1

Given:

• Number of blue pens = 14

,

• Number of black pens = 8

,

• Number of red pens = 6

Let's find the probability that the students will pick NOT a blue or a black pen.

To find the probability, we have the formula:

P(NOT a blue or black) = 1 - (P(blue) + P(black)

Where:

$\begin{gathered} P(\text{blue) = }\frac{\text{ number of blue pens}}{total\text{ number of pens}} \\ \\ P(\text{black)}=\frac{\text{ number of black pens}}{total\text{ number of pens}} \end{gathered}$

Where:

total number of pens = 14 + 8 + 6 = 28

Thus, we have:

$\begin{gathered} P(NOT\text{blue or black) = 1-(}\frac{14}{28}+\frac{8}{28}) \\ \\ P(NOT\text{ blue or black)=1-(}\frac{14+8}{28}) \\ \\ P(\text{NOT blue or black)=1-}\frac{22}{28} \end{gathered}$

Solving further:

$\begin{gathered} P(\text{NOT blue or black) = 1 - }\frac{11}{14} \\ \\ =1-\frac{11}{14} \\ \\ =\frac{1(14)-11(1)}{14} \\ \\ =\frac{14-11}{14} \\ \\ =\frac{3}{14} \end{gathered}$

Therefore, the probability is 3/14

ANSWER:

$\frac{3}{14}$