Question 362855
To pass the test he has to get at least 8 correct answers (40% of 20).  The probability of a correct answer is 1/5 = 0.20, a wrong answer, 4/5 = 0.80.
Therefore the probability that he passes is 
{{{1 - (matrix(2,1,20,0))*0.20^0*0.80^20  -(matrix(2,1,20,1))*0.20^1*0.80^19 -
(matrix(2,1,20,2))*0.20^2*0.80^18}}} - ... -{{{(matrix(2,1,20,7))*0.20^7*0.80^13}}}.