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 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 the color green and blue combined.
d) the color red is less likely to occur than the color green and blue combined.
e) it is twice as likely to spin a yellow as it is to spin a purple.

Explanation:

First, we calculate the total number of spins. The frequencies are: Green = 12, Yellow = 3, Blue = 15, Red = 4, Purple = 6. So total spins = \(12 + 3 + 15 + 4 + 6 = 40\).

Step 1: Analyze Option A

Frequency of green + yellow = \(12 + 3 = 15\). Frequency of blue = 15. So they are equal. So A is true.

Step 2: Analyze Option B

Frequency of blue = 15. Frequency of green + yellow + red + purple = \(12 + 3 + 4 + 6 = 25\). Wait, no, the statement is "The color green is more likely to occur than yellow, red and purple combined." Yellow + red + purple = \(3 + 4 + 6 = 13\). Green is 12. 12 < 13. So green is less likely than yellow, red, purple combined. So B is not true? Wait, no, let's re - check. Wait, the statement in B: "The color green is more likely to occur than yellow, red and purple combined." Yellow (3) + red (4) + purple (6) = 13. Green is 12. 12 < 13, so green is less likely. So B is not true? Wait, but let's check other options.

Step 3: Analyze Option C

Frequency of blue = 15. Frequency of green + yellow = \(12 + 3 = 15\). Wait, no, the statement is "It is 5 times as likely to spin a blue as it is to spin a green and blue combined." Wait, no, the statement is "It is 5 times as likely to spin a blue as it is to spin a green and blue combined"? Wait, no, the original statement: "It is 5 times as likely to spin a blue as it is to spin a green and blue combined" - no, that can't be. Wait, no, the statement is "It is 5 times as likely to spin a blue as it is to spin a green and yellow combined"? Wait, no, the user's text: "C) It is 5 times as likely to spin a blue as it is to spin a green and blue combined." Wait, that doesn't make sense. Wait, maybe a typo. Wait, looking at the frequencies: blue is 15, green is 12, yellow is 3, red is 4, purple is 6. Let's re - read option C: "It is 5 times as likely to spin a blue as it is to spin a green and blue combined." No, that would be blue vs (green + blue), which is impossible. Wait, maybe it's "green and yellow combined". Green + yellow = 12 + 3 = 15. Blue is 15. No, 15 is not 5 times 15. Wait, maybe "green and yellow combined" is 12 + 3 = 15, blue is 15. No. Wait, maybe the statement is "It is 5 times as likely to spin a blue as it is to spin a yellow". Yellow is 3, 5*3 = 15, which is blue's frequency. Oh! Maybe a typo in the problem statement. If it's "yellow" instead of "green and blue combined", then 5*3 = 15 (blue's frequency). But as per the given statement, "green and blue combined" is 12 + 15 = 27, and blue is 15, 15 is not 5 times 27. But this is confusing. Wait, let's check option D: "The color red is less likely to occur than the color green and blue combined." Green + blue = 12 + 15 = 27, red is 4. 4 < 27, so D is true.

Step 4: Analyze Option E

Frequency of yellow = 3, frequency of purple = 6. 6 is twice 3? No, wait, the statement is "It is twice as likely to spin a yellow as it is to spin a purple." Wait, no, yellow is 3, purple is 6. So it's twice as likely to spin purple as yellow. But the statement says "twice as likely to spin yellow as purple" which is false? Wait, no, maybe I misread. Wait, the statement: "It is twice as likely to spin a yellow as it is to spin a purple." Yellow: 3, Purple: 6. 3 is half of 6, so it's twice as likely to spin purple as yellow. So E is not true? But the question is which TWO statements are not true. Wait, let's re - calculate:

Total spins: 12 (green) + 3 (yellow) + 15 (blue) + 4 (red) + 6 (purple) = 40.

- Option A: Green + yellow = 12 + 3 = 15; Blue = 15. So equal. True.
- Option B: Green (12) vs Yellow + Red + Purple (3 + 4 + 6 = 13). 12 < 13, so green is less likely. So the statement "The color green is more likely to occur than yellow, red and purple combined" is false.
- Option C: If we assume the statement is "It is 5 times as likely to spin a blue as it is to spin a yellow" (maybe a typo), since blue is 15 and yellow is 3, 15/3 = 5. But as per the given statement "green and blue combined", green + blue = 27, 15/27 = 5/9 ≠ 5. So if we take the statement as given, C is false. But this is confusing. Wait, maybe the original statement is "It is 5 times as likely to spin a blue as it is to spin a yellow". Then C would be true. But as per the text, it's "green and blue combined".
- Option D: Red (4) vs Green + Blue (12 + 15 = 27). 4 < 27. True.
- Option E: Yellow (3) vs Purple (6). 3 is half of 6, so the statement "It is twice as likely to spin a yellow as it is to spin a purple" is false.

But the question says "which TWO statements are not true". Let's re - check the frequencies:

Green:12, Yellow:3, Blue:15, Red:4, Purple:6.

Option B: Green (12) vs Yellow + Red + Purple (3 + 4 + 6 = 13). 12 < 13, so the statement "green is more likely than yellow, red, purple combined" is false.

Option E: Yellow (3) vs Purple (6). The statement says "twice as likely to spin yellow as purple" - 3 is not twice 6 (6*2 = 12≠3), and 3 is half of 6, so it's twice as likely to spin purple as yellow. So E is false.

Wait, but maybe I made a mistake. Let's check option C again. The statement: "It is 5 times as likely to spin a blue as it is to spin a green and blue combined." Green + blue = 12 + 15 = 27. Blue is 15. 15/27 = 5/9, which is not 5. So C is false. But the question says TWO statements.

Wait, maybe the correct non - true statements are B and E (or B and C, or C and E). Let's re - evaluate:

Option B: Green (12) vs Yellow + Red + Purple (13). 12 < 13, so the statement "green is more likely" is false.

Option E: Yellow (3) vs Purple (6). The statement "twice as likely to spin yellow as purple" - 3 is not twice 6, so false.

Option C: If the statement was "It is 5 times as likely to spin a blue as it is to spin a yellow", then 15/3 = 5, which is true. But as per the given statement, it's "green and blue combined", so C is false.

But maybe there's a typo in the problem. Assuming that the intended statement for C was "It is 5 times as likely to spin a blue as it is to spin a yellow", then C is true. Then the non - true statements are B and E.

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