Probabilities on a spinner

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The discussion revolves around a math problem involving probabilities on a spinner, where the key question is whether the statement "3 has less than an even chance of coming up" is correct. Participants clarify that "less than even" typically means less than a 50% chance, rather than less than 1/3, which relates to the number of outcomes. The analogy of a fair coin toss is used to illustrate the concept of even chances. The consensus is that the interpretation of "less than even" aligns with the general understanding of probabilities. This clarification aids in understanding the problem for entrance exam preparation.
TensorCalculus
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Homework Statement
Bob says "3 has less than an even chance of coming up"
<diagram of spinner, attached below>
Is he right? Explain your answer.
Relevant Equations
N/A
My little sister was doing a practice maths paper (preparing for entrance exams into secondary schools) and she came across this question, which she got stuck on. As the one who marks her papers she asked me if I could help her: but the wording of this problem stumped me too. I don't have a mark scheme (though maybe one does exist), so I don't know what the correct answer is.

The problem goes as such:

Bob says "3 has less than an even chance of coming up"
(photo of spinner attached)
Is he right? Explain your answer.

What does the question mean by "less than even"? Does it mean less than 50%, or less than 1/3 (since there are three numbers on the wheel)?
 

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I think "less than 50%" would be the general interpretation of "less than even".
 
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TensorCalculus said:
What does the question mean by "less than even"? Does it mean less than 50%, or less than 1/3 (since there are three numbers on the wheel)?
Less than 50%. A toss of a fair coin has a 50% chance of a heads or a tails coming up.
 
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Ah okay, thank you! :smile:
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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