Odds of picking 10 in a row?

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Valdezdj

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What are the odds I could randomly, let's say out of a bingo machine, pick 10 true statements in a row when the machine has 7 false statements loaded and 8 true statements totaling 15 in all?
 
Valdezdj said:
What are the odds I could randomly, let's say out of a bingo machine, pick 10 true statements in a row when the machine has 7 false statements loaded and 8 true statements totaling 15 in all?
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What is a bingo machine? How does it function. After each pick does it does it reload( reset) to the 7/8 split?
 
Yes it reloads. Bingo machine is a tumbler with a handle to create randomness... the balls that represent true or false are color coded for distinction.
 
Valdezdj said:
What are the odds I could randomly, let's say out of a bingo machine, pick 10 true statements in a row when the machine has 7 false statements loaded and 8 true statements totaling 15 in all?
Click to expand...
My understanding is that such a machine selects randomly without replacement. There aren't 10 true statements. So the probability is 0.
Valdezdj said:
Yes it reloads. Bingo machine is a tumbler with a handle to create randomness... the balls that represent true or false are color coded for distinction.
Click to expand...
If you really mean selection with replacement, please show your work, so we can see what help you need:

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Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...
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Valdezdj said:
Yes it reloads. Bingo machine is a tumbler with a handle to create randomness... the balls that represent true or false are color coded for distinction.
Click to expand...
Thank you for the clarification. So it is sampling with replacement.
Hence \(\left(\dfrac{8}{15}\right)^{10}\) is the probability of ten straight trues.
 
The way the problem is written the answer is 0, as Dr Peterson said.
 
Valdezdj said:
Yes it reloads. Bingo machine is a tumbler with a handle to create randomness... the balls that represent true or false are color coded for distinction.
Click to expand...
Dr.Peterson said:
My understanding is that such a machine selects randomly without replacement. There aren't 10 true statements. So the probability is 0.

If you really mean selection with replacement, please show your work, so we can see what help you need:

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...
www.freemathhelp.com
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The bingo machine is just an example to illustrate a random pick.

The 10 picks are all true. Each pick has the exact same variables therefore "duplicates" exist when all 10 picks have transpired.

We'll visualize 7 blue (true) colored ping pong balls & 8 red (false) colored ping pong balls all mixed together in a glass-front household drying machine.

We turn it on, the we turn it off after its mixed the balls real well, open the door, without looking (to remove potential bias) we choose a ball, note the color and repeat 10 times.

How do we set up the equation and through that equation, how does one achieve a measure of probability to ascertain if the results are remarkably slim or not.

The results being all of the picks being blue (true).

I have math anxiety and although I'm willing to dive in I need a jump start to overcome my disability. This is why I'm unable to comply with your request for a status of the progress of my work. I'm not a student, however, this is a real event and I'm very interested in what the odds are. I found your site and thought it would be appropriate to ask.

I appreciate your help.

Thank you in advance.
 
You've actually been given the answer! See post #5.

Assuming (as you once again neglected to say) that the balls are put back after being chosen, and (as you said originally, as opposed to what you said just now) that there are 8 "true" balls, the probability for each individual ball being "true" is 8/15.

If each is independent, as would be true with replacement, then the probability of all 10 being true is [MATH](8/15)^{10} = 0.001862[/MATH], or 0.19%. That is a small probability, but far from impossible.

But people who ask this sort of question about something that actually happened commonly don't understand the meaning of probability, and apply it incorrectly. If you told us the real situation that lies behind your question, we could help you more effectively. Often something that seems very rare by itself turns out to be something that happens every day.

Here is a discussion on my blog (where I comment on questions asked at my former site) about such questions.
 
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