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A problem came up in a stats course I am taking. Suppose you have a population where $50\%$ of the population likes oranges and the rest hate oranges. What is the probability that a person chosen at random likes oranges? I said $50\%$, but they (professor) said that was incorrect. The answer they gave was $0.50$. Their reasoning was that $\%$ is a unit of measure, so $50\%$ is not a proportion which is what a probability must be. However, I thought that $50\%$ is a proportion. It is the number $\frac{50}{100}$. I then went to ask a TA for help. They mentioned that they use percentages when talking about chance and decimals for probability. I then asked what the difference is between chance and probability. They said that they use percentages when talking about chance and decimals for probability.

My question is why do this? Aren't percentages already proportions? Am I misunderstanding some kind of abstraction? They seem interchangeable.

Sebastian Osorio
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    Your professor is wrong. Percentage is no more of a unit than radians are in geometry. In fact, one percent is the name of the pure fraction $\frac{1}{100}$. – John Douma Feb 01 '23 at 18:37
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    That seems like an incredibly pedantic and arbitrary decision on their part. While I will agree that it is conventional to prefer to write probabilities without the use of the % symbol... it is by no means required and the literal interpretation of $50%$ and $0.5$ should be the same numerical object. "Percentages when talking about chance" But... chance is probability. It is just the more common colloquial word used by people less familiar with math terminology... – JMoravitz Feb 01 '23 at 18:39
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    If they insist on this... I'd recommend just keeping your head low and acquiescing, doing things how they want to for now, but know that as soon as you are out of that class you should be free to ignore what they said on this specific topic and do things the way the rest of the world does. – JMoravitz Feb 01 '23 at 18:40
  • To add to the above comments, % is not a unit of measure (what physical quantity is 8%?) but a postfix operator that divides by 100 such that 8% precisely equals 0.08, both of which are legitimate ways to specify the chance of rain tomorrow in my village. – ryang Feb 01 '23 at 19:27
  • I am sorry to hear that your professor takes such a narrow minded approach to right vs. wrong. – Godfather Feb 01 '23 at 21:51

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