Question

A bag is full of different colored marbles. The probability of randomly selecting a red marble from the bag is $\frac{1}{8}$. The probability of selecting a blue marble is $\frac{13}{24}$. Find each probability.

P (not blue)

Short answer

The probability of not getting a blue marble is $\frac{11}{24}$.

Step-by-step solution

Step 1. Apply the basic formula for probability of event not happening.

The probability of an event not happening is given by the following formula:

$\left(\begin{array}{l}\mathrm{Probability}\mathrm{of}\mathrm{an}\\ \mathrm{event}\mathrm{not}\mathrm{happening}\end{array}\right)=1-\left(\begin{array}{l}\mathrm{Probability}\mathrm{of}\mathrm{the}\\ \mathrm{event}\mathrm{happening}\end{array}\right)$

Step 2. Write the given information.

From the given information it can be seen that the probability of getting a blue marble from the bag is $\frac{13}{24}$.

Step 3. DESCRIPTION OF STEP.

In order to find the probability of not getting a blue marble substitute the value of the probability of getting a blue marble in the formula mentioned above.

$$\begin{gathered} P\left(\mathrm{Not}\mathrm{blue}\right)=1-P\left(\mathrm{Blue}\mathrm{marble}\right) \\ =1-\frac{13}{24} \\ =\frac{24-13}{24} \\ =\frac{11}{24} \end{gathered}$$

Hence, the probability of not getting a blue marble is $\frac{11}{24}$.