1. ## Probability Question

Hi,

A student is taking an exam consisting of four true-false questions. She is trying to guess the following probabilities:

a) All four questions are correct provided that she can answer the first question correctly but the remaining three questions are answered at random.

b) All four questions are answered correctly provided that she knows the correct answers of exactly three of them and only the remaining question is answered at random.

2. Originally Posted by shogunhd
Hi,

A student is taking an exam consisting of four true-false questions. She is trying to guess the following probabilities:

a) All four questions are correct provided that she can answer the first question correctly but the remaining three questions are answered at random.

b) All four questions are answered correctly provided that she knows the correct answers of exactly three of them and only the remaining question is answered at random.
a) If she knows the first answer, then you only have to worry about what's happening with three questions .....

So you want the probability of 3 correct guesses for 3 questions:

Pr(X = 3) where X follows a Binomial distribution with n = 3 and p = 1/2 ....... 1/8

--------------------------------------------------------------------------------------------------------------

b) If she knows all the answers except one, then you only have to worry about what's happening with that one question .....

So you want the probability of 1 correct guess for 1 question ..... 1/2.