joe took a 15-question multiple choice quiz with 4 alternatives for each question. what is the probability he will get 8 out of 15 questions correct by randomly guessing each answer? express as a percent.
A.) 0.3 %
B.) 1.3%
C.) 9.8%
D.) 53.3%
Please explain thanks!

Question

joe took a 15-question multiple choice quiz with 4 alternatives for each question. what is the probability he will get 8 out of 15 questions correct by randomly guessing each answer? express as a percent.
A.) 0.3 % 
B.) 1.3%
C.) 9.8%
D.) 53.3%
Please explain thanks!

anonymous · Answer

the probability of answering correct one question is 1/4 and wrong is 3/4;
now he has to correct 8 question so the probability of doing so is (1/4)^8 and he has to do 7 questions wrong at the same time so the probability of doing 7 question wrong is (1-1/4)^7=(3/4)^7
he can choose 8 questions out of five in 15C8 ways..
now the probability is (15C8)(1/4)^8(3/4)^7*100%=1.31%