A student takes a tenquestion truefalse exam round to four d

A student takes a ten-question true/false exam. (round to four decimal places.)

(a) Find the probability that the student gets exactly six of the questions right simply guessing the answer on every question.

(b) Find the probability that the student gets at least two questions correct simply by guessing

Solution

Binomial 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

a)
P( X = 6 ) = ( 10 6 ) * ( 0.5^6) * ( 1 - 0.5 )^4
= 0.2051
b)

P( X < 2) = P(X=1) + P(X=0)   
= ( 10 1 ) * 0.5^1 * ( 1- 0.5 ) ^9 + ( 10 0 ) * 0.5^0 * ( 1- 0.5 ) ^10
= 0.0107
P( X > = 2 ) = 1 - P( X < 2) = 0.9893