Question

A student takes a multiple choice test consisting of 5 questions where there are 4 choices per question. Also, each question is worth 20 points. Suppose the student guesses on each question. Let X be the number of questions the student gets correct. The probability distribution for X is given below. Find the probability that the student gets at least a 60 on the test. Give your answer to four decimal places.

Answer 1

Given problem under Binomial distribution

$p=\frac{1}{4}=0.25$ Let $q=1-p=0.75$ and $n=5$

To find $P(X\geq 3)$

$P(X\geq 3)=P(X=3)+P(X=4)+P(X=5)$

  

$=10(0.75)^{2}(0.25)^{3}+5(0.75)(0.25)^{4}+(0.25)^{5}$

   $=0.1035$