Question

Assume that random guesses are made for six multiple choice questions on an SAT test, so that there are n=6 trials, each with probability of success (correct) given by

p=0.4. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than

4.

P(X<4)= ________ (round to four decimal places)

Answer 1

X ~ B ( n = 6 , P = 0.4 )

P(X = 2) = CHP'Qin-r)

cm = n!/(n-)!c!


P(X =0) = C(0.4)(0.6) (6-0) = 0.0467


P(X = 1) = C(0.4)*(0.6)(6-1) = 0.1866


P(X = 2) = C(0.4)2(0.6) (6-2) = 0.3110


P(X = 3) = C(0.4)(0.6) (6-3) = 0.2765

P ( X < 4 ) = 0.8208

Answer 2

0.4557