Question

1. the probability of landing on purple on a certain spinner is $\frac{5}{8}$, and the probability of landing on either purple or pink is $\frac{19}{24}$. what is the probability of landing on just pink? why?

Explanation:

Step1: Recall probability formula

Let $P(Purple)=\frac{5}{8}$, $P(Purple\ or\ Pink)=\frac{19}{24}$. We use the formula $P(A\ or\ B)=P(A)+P(B)$ (assuming $A$ and $B$ are mutually - exclusive). Here, $P(Purple\ or\ Pink)=P(Purple)+P(Pink)$.

Step2: Rearrange formula to find $P(Pink)$

We can rewrite the formula as $P(Pink)=P(Purple\ or\ Pink)-P(Purple)$.
Substitute the given values: $P(Pink)=\frac{19}{24}-\frac{5}{8}$.
First, make a common denominator. Since $\frac{5}{8}=\frac{5\times3}{8\times3}=\frac{15}{24}$.
Then $P(Pink)=\frac{19}{24}-\frac{15}{24}=\frac{19 - 15}{24}=\frac{4}{24}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$