A multiple choice test consists of 5 questions, each question having 4 responses. There is only one correct response and the remaining 3 are incorrect responses. If a candidate attempts all the 5 questions then the probability that he answers at least 3 questions incorrectly is

Step-by-step solution

Given x=5, P= 1 4 , q= 3 4 P (at least there incorrect answer) aligned & = ^5 c ₃ ( 3 4 )^3 ( 1 4 )^2+ ^5 c ₄ ( 3 4 )^4 ( 1 4 )^1+ ^5 c ₅ ( 3 4 )^5 ( 1 4 ) & = ( 3 4 )^3 [ 5 4 2 1 16 +5 3 16 +1 9 16 ] & = 27 64 [ 10 16 + 15 16 + 9 16 ]= 27 64 34 16 & = 459 512 aligned