# Thread: Standard multiple choice probability, with elimination

1. ## Standard multiple choice probability, with elimination

A student is presented with a test consisting of standard multiple choice problems: each problem has four options, and they may select only one.

For each question, the student is able to eliminate two of the options, both of which he knows to be incorrect.

Once the student has eliminated the answers he knows to be incorrect, he guesses randomly between the remaining options.

What is the probability that the student will get at least a passing score of 70% on the test?

2. ## Re: Standard multiple choice probability, with elimination

Originally Posted by jbwtucker
A student is presented with a test consisting of standard multiple choice problems: each problem has four options, and they may select only one.

For each question, the student is able to eliminate two of the options, both of which he knows to be incorrect.

Once the student has eliminated the answers he knows to be incorrect, he guesses randomly between the remaining options.

What is the probability that the student will get at least a passing score of 70% on the test?
This is similar to your last question.

As 2 of the 4 are eliminated then p=0.5 and n= the total number of questions, do you know how many there is?

Then you need to find x s.t.

$\displaystyle P(x) = \binom{n}{x} 0.5^x\times 0.5^{n-x} \geq 0.7$