Questionare Probability

Question

Mark completes a survey which contains 3 questions. The answer to every question has to be yes or no. If there is a 60% chance of answering yes to each question, then calculate the probability that Mark:

a) Answers yes to every question

b) Answers no to at least two questions

c) Answers yes, no then yes to the three questions

Answer 1

Probabilty of 3 yesses is (.6)^3= .216

Probabilty of answering no to at least 2 questions can be done with the binomial expansion of (n+y)^3 where .4 is probability of n and .6 probability of yes

The expansion is n^3 +3(n^2y) +3(ny^2) + y^3. We are interested in the first 2 terms ( 3no’s and 2 no’s )

(.4)^3 + 3(.4^2 x .6)= .064 +.288 = .352

Prob of yes, then no, then yes= .6 x .4 x .6=.096