Question

the spinner above (with numbers 1, 2, 3, 4, 5, 6, 7, 8) is used in a game. what is the theoretical probability of the given event with one spin? p(a multiple of 3)
a. \\( \frac{3}{4} \\)
b. \\( \frac{1}{4} \\)
c. \\( \frac{3}{8} \\)
d. 0

Explanation:

Step1: Identify total outcomes

The spinner has 8 sections (numbers 1 - 8), so total possible outcomes \( n = 8 \).

Step2: Identify favorable outcomes

Multiples of 3 in 1 - 8 are 3 and 6. So number of favorable outcomes \( m = 2 \)? Wait, no: 3, 6, and wait, 3×1=3, 3×2=6, 3×3=9 (which is beyond 8). Wait, wait, the numbers on the spinner are 1,2,3,4,5,6,7,8. So multiples of 3: 3, 6. Wait, no, 3×1=3, 3×2=6, 3×3=9 (too big). Wait, but wait, maybe I made a mistake. Wait, 3 is a multiple of 3 (3×1), 6 is a multiple of 3 (3×2). Wait, but let's check again. Wait, the spinner has 8 equal parts? Wait, the diagram: the spinner is divided into 8 equal sectors? Wait, the numbers are 1,2,3,4,5,6,7,8. So total sections: 8. Now, multiples of 3 in these numbers: 3, 6. Wait, but wait, 3×1=3, 3×2=6, 3×3=9 (not in the list). So two numbers? Wait, no, wait the options: option b is \( \frac{1}{4} \) (which is 2/8), option c is 3/8. Wait, maybe I missed a number. Wait, 3, 6, and is there another? Wait, 3×1=3, 3×2=6, 3×3=9 (no). Wait, maybe the spinner is divided into 8 parts, but let's check the numbers again. Wait, the spinner has numbers 1,2,3,4,5,6,7,8. So multiples of 3: 3, 6. Wait, that's two numbers. But 2/8 = 1/4, which is option b. Wait, but wait, maybe I made a mistake. Wait, 3, 6, and is 9 there? No. Wait, maybe the spinner is divided into 8 equal sections, each with a number. So total outcomes: 8. Favorable outcomes: numbers that are multiples of 3. So 3 and 6: two numbers. So probability is 2/8 = 1/4. Wait, but let's check the options. Option b is 1/4. So that's the answer.

Wait, wait, maybe I miscounted. Let's list the numbers: 1,2,3,4,5,6,7,8. Multiples of 3: 3 (3×1), 6 (3×2). So two numbers. So probability is 2/8 = 1/4. So the correct option is b.

Answer:

b. \( \frac{1}{4} \)