Question

use the spinner to answer each question. give your answers as reduced fractions.

1. what is the probability that you spin the spinner and land on bankrupt?

1. what is the probability that you spin the spinner and receive at least 250 points?

Explanation:

Step1: Count total sections

The spinner has 12 equal - sized sections. We can see this by counting each colored/patterned part: Bankrupt, 250 (orange), 150 (blue), 500 (green), Lose Turn (purple), 250 (black), 100 (pink), 50 (yellow), 150 (orange), 500 (green), 50 (gray), 100 (blue), and Bankrupt (red). Wait, actually, let's count again carefully. Looking at the spinner, we can see that there are 12 distinct sections.

Step2: Solve for probability of Bankrupt

The number of favorable outcomes (landing on Bankrupt) is 1. The probability \( P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). So \( P(\text{Bankrupt})=\frac{1}{12} \).

Step3: Solve for probability of at least 250 points

First, identify the sections with at least 250 points. The sections with 250, 500, 250, 500. Let's count: the orange 250, black 250, green 500, green 500. Wait, let's list the values: 250 (orange), 500 (green), 250 (black), 500 (green - the other one). Wait, no, let's look at the spinner again. The sections with value ≥250: 250 (orange), 500 (green), 250 (black), 500 (the dark green one? Wait, no, let's count the number of sections with 250 or 500. The orange 250, black 250, green 500, dark green 500. Wait, actually, let's count:

• 250: two sections (orange and black)
• 500: two sections (green and dark green)

So total favorable outcomes = 2 + 2 = 4? Wait, no, wait the spinner: let's count the sections:

1. Bankrupt (1)
2. 250 (orange) (2)
3. 150 (blue) (3)
4. 500 (green) (4)
5. Lose Turn (purple) (5)
6. 250 (black) (6)
7. 100 (pink) (7)
8. 50 (yellow) (8)
9. 150 (orange) (9)
10. 500 (dark green) (10)
11. 50 (gray) (11)
12. 100 (blue) (12)

Wait, no, I think I miscounted earlier. Let's count the number of sections with value ≥250:

• 250: sections 2 and 6 (two sections)
• 500: sections 4 and 10 (two sections)

So total favorable = 2 + 2 = 4? Wait, no, wait section 2: 250, section 6: 250, section 4: 500, section 10: 500. So that's 4 sections. Wait, but let's check again. Wait, maybe I made a mistake. Wait, the spinner has 12 sections. Let's list all values:

1. Bankrupt
2. 250
3. 150
4. 500
5. Lose Turn
6. 250
7. 100
8. 50
9. 150
10. 500
11. 50
12. 100

Ah! Now I see. So the values:

• Bankrupt: 1
• 250: sections 2 and 6 (2)
• 150: sections 3 and 9 (2)
• 500: sections 4 and 10 (2)
• Lose Turn: 1
• 100: sections 7 and 12 (2)
• 50: sections 8 and 11 (2)

So for "at least 250" (≥250), the values are 250 and 500. Number of 250 sections: 2, number of 500 sections: 2. So total favorable = 2 + 2 = 4. Wait, but 2 + 2 = 4? Wait, no, 2 (250) + 2 (500) = 4. Then total outcomes = 12. So probability \( P=\frac{4}{12}=\frac{1}{3} \)? Wait, no, wait 4 divided by 12 reduces to \( \frac{1}{3} \)? Wait, no, 4/12 = 1/3? Wait, 4÷4 = 1, 12÷4 = 3. Yes. Wait, but wait, is that correct? Wait, let's check again. The sections with ≥250: 250 (2), 500 (2). So 4 sections. So 4/12 = 1/3.

Wait, but let's do the first part first.

1) Probability of Bankrupt:

Number of Bankrupt sections: 1. Total sections: 12. So \( P = \frac{1}{12} \).

2) Probability of at least 250 points:

Number of sections with ≥250: 2 (250) + 2 (500) = 4. Total sections: 12. So \( P=\frac{4}{12}=\frac{1}{3} \) (since we divide numerator and denominator by 4: 4÷4 = 1, 12÷4 = 3).

Answer:

s:

1. \(\frac{1}{12}\)
2. \(\frac{1}{3}\)