Question 1099938
The coefficients of {{{0.8W+0.2R}}} represent the probability of
being {{{Wrong}}} and being {{{Right}}} on each question.
The coefficients of
{{{(0.8W+0.2R)^6}}}={{{(0.8W)^6+6*(0.8W)^5*0.2*W^5*R+15(0.8)^4*(0.2)^2*W^4*R^2+"..."}}}={{{0.8^6*W^6+6*0.8^5*0.2*W^5*R+15*0.8^4*0.2^2*W^4R^2+"..."}}}
represent the probability of all the possible different outcomes for the 6-question test:
{{{0.8^6}}} is the probability of 6 wrong answers,
{{{6*(0.8)^5*0.2}}} is the probability of 5 wrong answers plus one right,
{{{15*(0.8)^4*(0.2)^2}}} is the probability of 4 wrong answers plus 2 right ones,
and so on.
So,the probability of getting less than 2 correct answers is
{{{0.8^6+6*0.8^5*0.2=0.8^5(0.8+6*0.2)=0.32768(0.8+1.2)=.32768*2=highlight(0.65536="65.536%")}}}