5. billy made the following line plot for the first 20 crayons he randomly pulled out of a bag. based on…

Explanation:

Step1: Count the number of each - color crayons

There are 6 purple crayons, 2 red crayons, 4 orange crayons, 1 yellow crayon, 2 brown crayons, and 5 blue crayons. The total number of crayons in the sample is 6 + 2+4 + 1+2 + 5=20.

Step2: Calculate the probability that the next crayon is red

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. For the event of getting a red crayon, the number of favorable outcomes is 2 (the number of red crayons in the sample), and the total number of outcomes is 20. So $P(\text{red})=\frac{2}{20}=\frac{1}{10}$.

Step3: Calculate the probability that the next crayon is not purple

The number of purple crayons is 6. The number of non - purple crayons is 20 - 6 = 14. Using the probability formula, $P(\text{not purple})=\frac{14}{20}=\frac{7}{10}$. The reason is that the probability of an event not occurring is 1 minus the probability of the event occurring. The probability of getting a purple crayon is $\frac{6}{20}$, so the probability of not getting a purple crayon is $1-\frac{6}{20}=\frac{20 - 6}{20}=\frac{14}{20}=\frac{7}{10}$.

Answer:

a) $\frac{1}{10}$ b) $\frac{7}{10}$, because the probability of an event not occurring is 1 minus the probability of the event occurring. The probability of getting a purple crayon is $\frac{6}{20}$, so the probability of not getting a purple crayon is $1 - \frac{6}{20}=\frac{14}{20}=\frac{7}{10}$.