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?

Re: Standard multiple choice probability, with elimination

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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.

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