Probability of Answering True/False Questions?

Question

A student makes random guesses for 10 true/false questions. What is the probability of getting one correct answer?

I can't seem to get the logic figured out on this one. Can someone set me in the right direction?

Thanks

I was looking for a little more explanation. Remember it is the odds of answering one out of the 10 correctly.

I need the explanation in fractions also. This is a review question for a midterm and I want to get it figured out in my head. Not just looking for the answer.

Thanks again!

Ok...how do I accept the correct answer?

Its just the Probability of Answering ONE question correctly.

Northstar got the answer correct. Now I wish I could figure out how to give him credit. WHERE IS THE ACCEPT ANSWER?????

Answer 1

I assume you mean, what is the probability that at least one of the ten answers is correct. If this is the case then:

Probability = 1 - Probability(All are wrong)

= 1 - (1/2)^10 = 1 - 1/1024 = 1023/1024

Answer 2

Random True Or False Questions

Answer 3

OK

I am not going to throw around answers like everyone here since your question needs to be a little more specific:

Do you want the probability of getting AT LEAST one right OR

Do you want the probability of getting ONLY one right.


The final answer is different depending upon your answer to this question. The first one has a very high probability (I think some one showed like 97%). The second has a much lower probability (like 9 out of 1,024).

SO you can see why you are getting so many different answers. Make sure you pick which one you want.

Hope that helps.

Answer 4

1/2

Answer 5

The chance of getting any one question correct is 1/2. The chance of getting the question wrong are likewise 1/2. The chance that he gets the first question right but the remaining questions wrong are therefore (1/2)^1 * (1/2)^(10-1) or 1/1024.

However, this is only one of ten ways the student can get exactly one question right. It need not be the first question he gets right, it can be any one of the ten. There are thus ten distinct ways to get exactly one question right. The correct answer is therefore 10 * (1/2)^10, or 5/512.

Answer 6

Ok if you randomly answer one TF question, you have a 50% chance of getting one right.

To answer two randomly, There is one chance out of 4 that you will get both wrong, so there is a 75% chance of getting one right (at least one)

Three randomly, there is only one way you can get all three wrong...Let R represent a right answer and W a wrong answer

RRR RRW RWR RWW WRR WRW WWR WWW

So there is a 7/8 chance of getting at least one right

87.5% chance

See a pattern forming? To get the next term, you take the term, then add half of (100-term)

So for 4 we get 93.75%

5 => 96.875%

6 => 98.4375%

7 => 99.21875%

8 => 99.609375%

9 => 99.8046875%

10=> 99.90234375%

So by rounding we get 99.9% chance that by randomly guessing T/F for a set of ten problems, we will get at least one correctly.

Answer 7

first off, the probablity of getting a correct answer is 1/2.
and the probability of getting an incorectin answer is 1/2

The question ask for the probablity of getting 1 correct answer. In other words, it ask for the probablity of getting 1 correct answer and 9 incorrect answer

P = (1/2)^1 (1/2)^9

but that student can answer any 1 out of 10 question right.
so there are 10C1 = 10 ways to do so

P = 10(1/2)(1/2)^9
P = 5/512 <== answer

Answer 8

1 out of 10.

Answer 9

He's got a 50/50 chance of answering one question correctly.
He's got a 1 in ten shot at answering ANY of them correct because there's ten questions and he's working on one question. Each question has a 50% chance of being right.

Answer 10

success p = .5 (because it's true or false)
failure q = .5

n choose r (10,1) = 10

10 * .5^1 * .5^(10-1)
(Means 10 questions, one correct, 9 incorrect)

= .00977

.977 %

RE: Kid, I'm right trust me. I teach stats at a college.
RE: Northstar is not correct. You said one correct, NOT at least one correct. He made a false assumption out of nowhere.