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1. chelsea has a spinner with 7 equal sections. she spun the spinner mu…

Question

  1. chelsea has a spinner with 7 equal sections. she spun the spinner multiple times and recorded the results below.

spinner results
color | frequency
green | 12
yellow | 3
blue | 15
red | 4
purple | 6

based on the results, which two statements are not true?

a. there is an equal chance of spinning a green or a yellow combined as it is to spin a blue.

b. the color green is more likely to occur than yellow, red, and purple combined.

c. it is 5 times as likely to spin a blue as it is to spin a yellow.

d. the color red is less likely to occur than the colors green and blue combined.

e. it is twice as likely to spin a yellow as it is to spin a purple.

Explanation:

Response

To solve this, we analyze each option using the spinner frequencies: Green = 12, Yellow = 3, Red = 4, Blue = 15, Purple = 6.

Option A

Green + Yellow = \( 12 + 3 = 15 \), Blue = 15. So \( 15 = 15 \), A is true.

Option B

Green = 12; Yellow + Red + Purple = \( 3 + 4 + 6 = 13 \). Since \( 12 < 13 \), Green is not more likely. B is false.

Option C

Blue = 15, Yellow = 3. \( \frac{15}{3} = 5 \), so Blue is 5× more likely. C is true.

Option D

Red = 4; Green + Blue = \( 12 + 15 = 27 \). Since \( 4 < 27 \), Red is less likely. D is true.

Option E

Yellow = 3, Purple = 6. \( \frac{6}{3} = 2 \), so Purple is 2× more likely (i.e., Yellow is half as likely as Purple, or Purple is twice as likely as Yellow—wait, the option says: "It is twice as likely to spin a yellow as it is to spin a purple." But \( 3 \) (yellow) is not twice \( 6 \) (purple). Wait, no—wait, \( \text{Yellow} = 3 \), \( \text{Purple} = 6 \). So \( \text{Purple} = 2 \times \text{Yellow} \), meaning it is twice as likely to spin purple as yellow. But the option says "twice as likely to spin yellow as purple"—which is false? Wait, no, let's recheck.

Wait, the option E: "It is twice as likely to spin a yellow as it is to spin a purple." So \( P(\text{yellow}) = 2 \times P(\text{purple}) \)? But \( 3 \) (yellow) vs. \( 6 \) (purple): \( 3 = 2 \times 6 \)? No, \( 6 = 2 \times 3 \). So actually, it is twice as likely to spin purple as yellow. Thus, option E is false? Wait, but the question asks "which two statements are not true?" Wait, maybe I made a mistake. Wait, let's re-express frequencies as counts (since probability is proportional to frequency here).

Wait, the problem says "which two statements are not true?" Wait, the original problem might have a typo, but let's re-express:

Wait, the frequencies are: Green:12, Yellow:3, Red:4, Blue:15, Purple:6. Total spins: \( 12 + 3 + 4 + 15 + 6 = 40 \). But we can use counts directly for likelihood (since all sections are equal, but the spinner was spun multiple times—so frequency ≈ probability).

Wait, let's re-analyze E: "It is twice as likely to spin a yellow as it is to spin a purple." So \( \text{Frequency(Yellow)} = 2 \times \text{Frequency(Purple)} \)? \( 3 = 2 \times 6 \)? No, \( 6 = 2 \times 3 \). So actually, purple is twice as likely as yellow. Thus, E is false. But earlier, B was also false. Wait, the question says "which two statements are not true?" So B and E? Wait, but let's recheck B: "The color green is more likely to occur than yellow, red, and purple combined." Yellow + Red + Purple = \( 3 + 4 + 6 = 13 \). Green = 12. So 12 < 13, so green is less likely than yellow+red+purple. Thus, B is false. E: "twice as likely to spin yellow as purple"—yellow is 3, purple is 6. 3 is half of 6, so it is twice as likely to spin purple as yellow. Thus, E is also false. Wait, but maybe I misread E. Let me check again: "It is twice as likely to spin a yellow as it is to spin a purple." So \( P(\text{yellow}) = 2 \times P(\text{purple}) \). But \( P(\text{yellow}) = 3/40 \), \( P(\text{purple}) = 6/40 \). \( 3/40 = 2 \times 6/40 \)? No, \( 3/40 = 1/2 \times 6/40 \). So E is false.

But the original problem might have intended to ask which two are not true. From the options, B and E are not true? Wait, but let's confirm:

  • A: Green + Yellow = 15, Blue = 15 → true.
  • B: Green (12) vs. Yellow+Red+Purple (13) → 12 < 13 → false.
  • C: Blue (15) vs. Yellow (3) → 15/3 = 5 → true.
  • D: Red (4) vs. Green+Blue (27) → 4 < 27 → true.
  • E: Yellow (3) vs. Purple (6) → 3 is not twice 6 (6 is twice 3) → false.

So the tw…

Answer:

B. The color green is more likely to occur than yellow, red, and purple combined.
E. It is twice as likely to spin a yellow as it is to spin a purple.