Question

(1 point) A quiz consists of 10 multiple-choice questions, each with 4 possible answers. For someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %. P(pass) = Use four decimals.

Answer 1

BIONOMIAL DISTRIBUTION pmf of B.D is = f(k) = (n k) p^k* (1-p) ^n-k where k = number of successes in trials n = is the number of independent trials p = probability of success on each trial probability minimum passing grade is 50% i.e P(X>5) it is given, N=10, p = 1/4 = 0.25 probability of passing if the minimum passing grade is 50%, student should get atleast 5 right answers PCX < 5) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0) = (10 4) * 0.25^4 * (1-0.25) ^6+ (10 3) * 0.25^3* (1-0.25 ) ^7 + ( 10 2) * 0.25^2 * (1-0.25) 18+ (101) * 0.25^1* ( 1-0.25 ) ^9+ (100 ) * 0.25^0 * (1-0.25) 410 = 0.921873 P(X > = 5 ) = 1 - P(X< 5) = 0.078127