[Shazer]

Puzzle:
There are seventeen questions.
Sixteen of the answers given are wrong.
What are the odds that 16 of 17 answers would be wrong?

Given...
The probability of getting a right answer is: 0.5

I believe it goes like this...
The probability of getting 16 in a row wrong = 0.5 to the 15th power.

Then, I get lost on how to translate that answer into a fraction and then odds.

I believe the answer is something like over 65,000 to 1.

Can anyone demonstrate the proper math?

[xyz]

The answer is 17*(0.5)^17=0.0001297

[MonkeyF0cker]

Google combinations and permutations, Shazer.

[u21c3f6]

The answer is 17*(0.5)^17=0.0001297

+1

Joe.

[Dimwhit]

Puzzle:
There are seventeen questions.
Sixteen of the answers given are wrong.
What are the odds that 16 of 17 answers would be wrong?

Given...
The probability of getting a right answer is: 0.5

I believe it goes like this...
The probability of getting 16 in a row wrong = 0.5 to the 15th power.

Then, I get lost on how to translate that answer into a fraction and then odds.

I believe the answer is something like over 65,000 to 1.

Can anyone demonstrate the proper math?

Not sure what your question is...seems like you ask a couple.

1) Probably of getting 16 in a row wrong:

1 : 2^16 = 1 : 65532

2) What are the odds that 16 of 17 answers would be wrong?

Seems that you want to know what the probability of getting exactly one answer wrong in 17 tries, not just getting the last one wrong.

So, there are 2^17 possible combinations = 131072

Each specific outcome, e.g., getting the first right followed by 16 wrong, has the probability of 1:131072.

There are 17 possible ways you can get one answer right, but miss the rest as follows:
1) 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2) 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3) 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
....
17) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1


So, the probability that you should get one correct answer and 16 wrong answers is:
17 : 131072

Well, that's my guess at least.

[Shazer]

"1) Probably of getting 16 in a row wrong:

1 : 2^16 = 1 : 65532"


Thanks, that's what I needed to be verified!

[u21c3f6]

"1) Probably of getting 16 in a row wrong:

1 : 2^16 = 1 : 65532"


Thanks, that's what I needed to be verified!

Just to clarify, please note that the above does not answer your qustion of: "What are the odds that 16 of 17 answers would be wrong?"

That answer is: 17*(0.5)^17=0.0001297 or 1 : 7710

Joe.

[MonkeyF0cker]

"1) Probably of getting 16 in a row wrong:

1 : 2^16 = 1 : 65532"


Thanks, that's what I needed to be verified!

Uhh. That's not the right answer to that question either. It's 65,535:1.

[Justin7]

Just to clarify, please note that the above does not answer your qustion of: "What are the odds that 16 of 17 answers would be wrong?"

That answer is: 17*(0.5)^17=0.0001297 or 1 : 7710

Joe.

u21/Joe... are correct.

[MonkeyF0cker]

They are correct except that the ratio is 7709:1, not 7710:1.