Question

you spin the spinner once.
what is p(odd or greater than 7)?
write your answer as a fraction or whole number.

Explanation:

Step1: Identify total outcomes

Total sections = 4, so total possible outcomes: $n(S)=4$

Step2: Define event sets

• Odd numbers: $A = \{5,7\}$, so $n(A)=2$
• Numbers >7: $B = \{8\}$, so $n(B)=1$
• No overlap ($A\cap B=\emptyset$), so $n(A\cap B)=0$

Step3: Apply addition rule

Use $P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$$\begin{align*} P(A\cup B)&=\frac{n(A)}{n(S)}+\frac{n(B)}{n(S)}-\frac{n(A\cap B)}{n(S)}\\ &=\frac{2}{4}+\frac{1}{4}-\frac{0}{4} \end{align*}$$

Step4: Calculate final probability

Sum the fractions: $\frac{2+1-0}{4}=\frac{3}{4}$

Answer:

$\frac{3}{4}$