True or False Probabilty Question

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bubbagump

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An exam consists of 20 true-or-false questions. If a student guesses at every answer, what is the probability that he or she will answer exactly 12 questions correctly? (Round your answer to three decimal places.)

So I'm not exactly sure how to do this:
20(.5)^12

or is it:
(12/20) (11/19) ... (1/8) ??

Can you help me set it up?? Thank you!
 
bubbagump said:
An exam consists of 20 true-or-false questions. If a student guesses at every answer, what is the probability that he or she will answer exactly 12 questions correctly? (Round your answer to three decimal places.)

So I'm not exactly sure how to do this:
20(.5)^12

or is it:
(12/20) (11/19) ... (1/8) ??

Can you help me set it up?? Thank you!
Click to expand...

Have you worked with binomial distribution?
 
Yes I've used it before but I haven't used it for any other problem yet...
Can you refresh my memory on how to do it? We did it in the beginning of the year. Thanks.
 
bubbagump said:
Yes I've used it before but I haven't used it for any other problem yet...
Can you refresh my memory on how to do it? We did it in the beginning of the year. Thanks.
Click to expand...

If the probabbility of an event is p, then probability of occurring r out of n times is:

\(\displaystyle _nC_r \ * \ (p)^r * (1-p)^{n-r}\)
 
Are there any other ways to do this problem? I feel like this isn't what we're supposed to do.
The section this is under is use of counting techniques.

So if I were to use the other part...
What would be p?
12 would be r and 20 would be n, right?
 
The binomial is the way to go with this one.

Choose 12 out of the 20 to get correct. \(\displaystyle \binom{20}{12}\)

The probability that 12 are correct is \(\displaystyle (\frac{1}{2})^{12}\)

The others are incorrect, \(\displaystyle (\frac{1}{2})^{20-12}\)

Multiply it all together.

Thus, we have the binomial probability.

\(\displaystyle \binom{n}{k}p^{k}(1-p)^{n-k}\)
 
I keep getting a huge number. Why is this? I'm pretty sure its supposed to be a decimal....
 
bubbagump said:
I keep getting a huge number. Why is this? I'm pretty sure its supposed to be a decimal....
Click to expand...

We don't know WHY this is, since you did not show us your work.... Since you were given the formula you need to use, and you have all of the numbers that are required in this formula, it would appear that you've got an arithmetic mistake somewhere. Please show us how you did the arithmetic, along with any "intermediate" answers you got in the process.

And yes, the answer SHOULD be a decimal....
 
Hello, bubbagump!

I keep getting a huge number. Why is this?
Click to expand...

It's hard to see your work from here . . .


\(\displaystyle \text{It looks like you played the }K\clubsuit\text{ instead of the }7\heartsuit\).

. . \(\displaystyle \text{and transposed to the key of }F\sharp\text{ major instead of }B\flat\text{ minor.}\)

. . \(\displaystyle \text{and you should have ended the routine with a double Axil.}\)

 
Sorry! I didn't specify. I got it. I had a calculator error. I accidentally put in a wrong number. :( Thanks for all the jokes! Made my day! lol
 
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