Question

1. the spinner shown is divided into congruent sections. if the spinner is spun one time, what is the probability of the arrow not landing on a section labeled a or b?

a (\frac{5}{9})
b (\frac{2}{3})
c (\frac{1}{3})
d (\frac{2}{9})

Explanation:

Step1: Count total sections

Total congruent sections = 9

Step2: Count A/B sections

Number of A sections = 2, Number of B sections = 3. Total A or B sections = $2 + 3 = 5$

Step3: Calculate non-A/B probability

Probability of NOT A/B = $1 - \frac{\text{Number of A/B sections}}{\text{Total sections}}$
$1 - \frac{5}{9} = \frac{4}{9}$? No, correction: Wait, total non A/B sections = $9 - 5 = 4$? No, wait count sections: A(2), B(3), C(2), D(1). $2+3+2+1=9$. Non A/B = $2+1=3$. Oh, correct count: Non A/B sections = 3. Probability = $\frac{3}{9} = \frac{1}{3}$
Wait, recheck:

Step1: Total sections count

Total sections = 9

Step2: Count A and B sections

A: 2, B: 3. Sum: $2+3=5$

Step3: Compute non-A/B probability

Probability = $\frac{\text{Total} - \text{A/B count}}{\text{Total}} = \frac{9-5}{9} = \frac{4}{9}$? No, no, count the spinner:
Looking at spinner: sections are A, C, B, A, B, B, B, C, D. Wait no, let's count again:

1. A
2. C
3. B
4. A
5. B
6. B
7. B
8. C
9. D

Yes, A:2, B:4? Oh! I miscounted B. B sections: 4. So A+B=2+4=6. Then non A/B = 9-6=3. Probability = $\frac{3}{9} = \frac{1}{3}$
Correct step:

Step1: Count total sections

Total congruent sections = 9

Step2: Count A and B sections

Number of A = 2, Number of B = 4. Total A or B = $2+4=6$

Step3: Calculate non-A/B probability

Probability = $\frac{9-6}{9} = \frac{3}{9} = \frac{1}{3}$

Answer:

C. $\frac{1}{3}$