Question

(b) Only one of the sets can contain all five correct answers. If you are guessing, so that you are as likely to choose one sequence of answers as another, what is the probability of getting all five answers correct

Answer 1

Solution :

Given that there is only one set which can contain all the five correct answers. While guessing that I am likely to choose only one sequence of the answers as another, then the probability of getting all the five answers correct  is given by :

Given : X $\sim$ binomial $\left( 5 , \frac{1}{3} \right)$

P (X = 5)

$= \ ^5C_5\left({\frac{1}{3}\right)^5\left(\frac{2}{3}\right)^0$

= 0.00412

Thus the probability is 0.00412