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

Solving further:

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

Therefore, the probability is 3/14

ANSWER:

`(3)/(14)`