Question

You are taking a short 4 question pop adz o er material you forget to study fortatoestion is multple choice with 5 po bleanove. These q estius se rainthetiak tD 4 decimal places and indoka leadinerem. (Exanele".179" ป ould be written an . 179n. 5esre that -neeach soidmaadeos a The probability that you guess correctly on all 4 quetions is b The probability that you puess incorrectly on all 4 questions is C The probability that you get at least one of the questions wrong ts d The probability that your first correct question is on the 3rd question i

Answer 1

$a.~Let~X=random~variable~denoting~no.~of~correct~answers\sim Binomial(4,1/5)\\ Since~probability~of~success~for~each~question~is~fixed~and~i.e.~1/5~and~answering\\ ~each~question~is~independent~to~each~others.\\ a.~P(X=4)=(1/5)^4=0.0016\\ b.~P(X=0)=(4/5)^4=0.4096\\ c.~Let~Y=random~variable~denoting~no.~of~wrong~answers\sim Binomial(4,4/5)\\ P(Y\geq 1)=1-P(Y=0)=1-(1/5)^4= 0.9984\\ d.~Probability~that~your~first~correct~question~is~the~3rd~question\\ =P(\{WWCC\})+P(\{WWCW\})~where~W~stands~for~wrong~question~and~C~\\ stands~for~correct~question.\\ =(1/5)^2*(4/5)^2+(1/5)^3*(4/5)~since~outcomes~are~independent\\ =0.0320$