Question

There are 42 questions , there are 5 answers to each question, only 1 is correct . To pick 1 answer at random what is the chance of getting 30 questions right?

Answer 1

`C_(42,30)(1/5)^30(4/5)^12~~8.2xx10^-13`

Explanation:

This can be solved with a binomial probability:

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

We're looking specifically at getting 30 questions out of 42 correct, giving `n=42, k=30`. For each question, the probability of getting it correct is `1/5` and therefore getting it incorrect is `4/5`, giving `p=1/5 and ~p=4/5`:

`C_(42,30)(1/5)^30(4/5)^12~~(11,058,116,888)(1.07xx10^-21)(.0687)~~8.2xx10^-13`