MHB See if you can create a valid answer

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The discussion revolves around a teacher's claim that in a class of 34 students, none having the surname Potato, is statistically rare given that 3% of the population has this surname. Participants are encouraged to provide mathematical proof to support or refute this claim. The probability that a given person does not have the surname Potato is 0.97, and the discussion touches on the concept of independent events in probability. Users are reminded to maintain the integrity of the thread by not deleting original content after resolution. Engaging in this mathematical puzzle can enhance the forum's knowledge base.
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So here's a question for you all.

There was once a teacher who said
"According to a recent census, 3% of the population in our country has the surname Potato. That's in a ratio of 1 to 33 people. This class has 34 people in it, but none of you have the surname Potato. Pretty rare, isn't it?"

Explain whether you agree or not with mathematical proof.
 
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Hi, and welcome to the forum.

Yuugen0127 said:
So here's a question for you all.
This phrase sounds like you already know the answer and want to offer this question as a puzzle. If this is the case, then you should post it to the http://mathhelpboards.com/challenge-questions-puzzles-28/. Be sure you do know the answer! If, on the other hand, you need help with the solution, then you should describe what you know about the subject, what you have tried and what your difficulty is. Please see forum http://mathhelpboards.com/rules/ in this regard (click "Expand" on top).

Yuugen0127 said:
There was once a teacher who said
"According to a recent census, 3% of the population in our country has the surname Potato. That's in a ratio of 1 to 33 people. This class has 34 people in it, but none of you have the surname Potato. Pretty rare, isn't it?"

Explain whether you agree or not with mathematical proof.
Note that the probability that a given person is not a Potato is 0.97. Also, $P(A\text{ and }B)=P(A)P(B)$ if $A$ and $B$ are independent events.
 
Yuugen0127 said:
So here's a question for you all.

There was once a teacher who said
"According to a recent census, 3% of the population in our country has the surname Potato. That's in a ratio of 1 to 33 people. This class has 34 people in it, but none of you have the surname Potato. Pretty rare, isn't it?"

Explain whether you agree or not with mathematical proof.

I have restored your posts' original content. Please DO NOT edit the first post of a thread you have begun to remove the content...this renders the thread useless. One of the things we value most here are threads with questions that are then discussed and hopefully brought to resolution. So, rather than come along and delete the question when you have resolved it, post your solution for the benefit of others who may find your thread. This enriches our site and does not leave threads with gutted content.
 
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