Question

the spinner is equally likely to land on any of the five sections. what is the probability that the spinner lands on an even number or on the unshaded section? 1/5 2/5 3/5 4/5

Explanation:

Step1: Identify total number of outcomes

The spinner has 5 sections, so the total number of possible outcomes is $n = 5$.

Step2: Identify favorable outcomes for even - numbered sections

The even - numbered sections are 2 and 4. So the number of even - numbered sections $n_{even}=2$.

Step3: Identify favorable outcomes for unshaded sections

Let's assume the unshaded section is 1. So the number of unshaded sections $n_{unshaded}=1$.

Step4: Check for overlapping outcomes

There is no overlap between the set of even - numbered sections and the unshaded section.

Step5: Calculate the probability

Using the addition rule for mutually - exclusive events $P(A\cup B)=P(A)+P(B)$. The probability of landing on an even number $P(even)=\frac{n_{even}}{n}=\frac{2}{5}$, and the probability of landing on the unshaded section $P(unshaded)=\frac{n_{unshaded}}{n}=\frac{1}{5}$. Then $P(even\cup unshaded)=\frac{2 + 1}{5}=\frac{3}{5}$.

Answer:

$\frac{3}{5}$