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 $P(A\ or\ B)=P(A)+P(B)$ for mutually - exclusive events. Here, $P(Purple\ or\ Pink)=P(Purple)+P(Pink)$.

Step2: Solve for $P(Pink)$

We can rewrite the formula as $P(Pink)=P(Purple\ or\ Pink)-P(Purple)$. First, make the common denominator for $\frac{5}{8}$ and $\frac{19}{24}$. Since $\frac{5}{8}=\frac{5\times3}{8\times3}=\frac{15}{24}$, then $P(Pink)=\frac{19}{24}-\frac{15}{24}$.

Step3: Calculate the result

$P(Pink)=\frac{19 - 15}{24}=\frac{4}{24}=\frac{1}{6}$. The reason is that for mutually - exclusive events (a spinner can't land on purple and pink at the same time), the probability of the union of two events is the sum of their individual probabilities.

Answer:

$\frac{1}{6}$