Calculating Probability of Correct Answers on Multiple Choice Questions

[th3whit3fang]

Homework Statement

You have got 10 multiple choice questions with 3 possible choices per question. What is ur chance that you will have 5 answers correct?

So the chance for a correct answer per question is 1/3 and for an uncorrect answer per question is 2/3.

The Attempt at a Solution

correct solution:

10 nCr 5 * (1/3)^5 * (2/3)^5 = 896/6561

(with 10 nCr 5 = combination with n= 10 and k = 5 )

I don't know how to get to the solution.

THank u

 

[Curious3141]

Homework Statement

You have got 10 multiple choice questions with 3 possible choices per question. What is ur chance that you will have 5 answers correct?

So the chance for a correct answer per question is 1/3 and for an uncorrect answer per question is 2/3.

The Attempt at a Solution

correct solution:

10 nCr 5 * (1/3)^5 * (2/3)^5 = 896/6561

(with 10 nCr 5 = combination with n= 10 and k = 5 )

I don't know how to get to the solution.

THank u

The expression is a simple application of Binomial probability. The final answer is just a simplification by cancellation of common factors.

You first *choose* 5 questions that you get right. The other 5 are automatically decided by elimination. Then you figure out the probability of getting the 5 that you chose right and the other 5 wrong. Can you now see why the expression has that particular form?

 

[th3whit3fang]

thank u