Question

1. On a multiple choice exam with 4 possible answers for each of 7 questions, what the probability that a student will get 6 or more correct just by guessing randomly? (Hint: the student has an independent 1/4 chance of answering each individual question successfully.)

Answer 1

TOPIC:Binomial distribution.

1.7 Define, n = Total no. of questions = 7; p =P (of guessing connectly). 1 There are 4 possible answers for each - questions, among which) only one is true. Number of questions, answered correctly by the student. Let, x= X ~ Bin (n = 7, 8 = 4 So, the poof of x is - - P(x+2) = { (1) (+)*(*) 72 ; dom, ; Jor, 220,1,277 s otherwise. Now, we need. 27 P ( x is 6 or more), = P(x76). =P ( X = 6) + (x = 7). = (?) (+) 3 ( 2 ) + (14) = N 0.001343 o. 0013 Can,