Question

it is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. if the pointer lands on a borderline, spin again. find the probability that the pointer will stop on an even number or a number greater than 3. the probability is \boxed{}. (type an integer or a fraction. simplify your answer.)

Explanation:

Step1: Identify even numbers

Even numbers from 1 - 8: 2, 4, 6, 8. So 4 numbers.

Step2: Identify numbers > 3

Numbers > 3 from 1 - 8: 4, 5, 6, 7, 8. So 5 numbers.

Step3: Identify overlap (even and >3)

Overlap: 4, 6, 8. So 3 numbers.

Step4: Apply inclusion - exclusion principle

Probability of A or B: \( P(A\cup B)=P(A)+P(B)-P(A\cap B) \)
\( P(A)=\frac{4}{8} \), \( P(B)=\frac{5}{8} \), \( P(A\cap B)=\frac{3}{8} \)
\( P(A\cup B)=\frac{4 + 5- 3}{8}=\frac{6}{8}=\frac{3}{4} \)

Answer:

\(\frac{3}{4}\)