A kid takes a test with 25 multiple choice questions and each question has four choices. If he gueses at all 25 questions, what is the probability he gets between 8 and 12 correct?

Question

779 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-18T01:48:50

I got #~~0.2701~~27%#

This is a binomial probability question. We'll use the form:

#sum_(k=0)^(n)C_(n,k)(p)^k(~p)^(n-k)#

to find our answer.

Each term of the summation refers to one instance of probability - with #k=0#, for example, we get the probability of getting 0 answers correct.

We're looking at #8<=k<=12#, so 5 terms that we'll sum.

There are 4 choices with 1 being correct, and so there are 3 incorrect, with 25 questions in total, therefore:

#n=25, p=1/4, ~p=3/4#

#C_(25,8)(1/4)^8(3/4)^17+C_(25,9)(1/4)^9(3/4)^16+C_(25,10)(1/4)^10(3/4)^15+C_(25,11)(1/4)^11(3/4)^14+C_(25,12)(1/4)^12(3/4)^13~~0.2701~~27%#