- #1

Philip Wong

- 95

- 0

## Homework Statement

Midvale School for the Gifted has two types of students: Guessers and Swots. All

Midvale tests consist of sets of questions with yes/no answers. Guessers will simply

answer yes or no to each question as the mood takes them, so they have probability

0.5 of getting each question correct. Swots, on the other hand, will certainly get

every question correct with probability 1. Dr Ramble Fluster is the Chief Examiner

at Midvale. She worries about her test results. Clearly, all Swots will get 100% on

every test. However, it is possible that a Guesser might get 100% just by chance.

Ramble's job is to decide how many questions to set in each test to be fairly certain

that she will be able to give the correct grade (G or S) to each student.

(b) What is the probability that a Guesser scores 100% on a test with n questions?

## Homework Equations

Binomial function

## The Attempt at a Solution

X~Bin(n,0.5)

P(X=x)= nCx * p^x * (1-p)^(n-x)

P(X=100) = nC100 * 0.5^100 * 0.5^(n-100)

here is where I got stuck. Since the question is asking us to solve the probability equation (P(X=x)), but since n is an unknown I don't know how to go further into solving this equation, because (I presume) there will be 2 unknown parameters: P and n.

can someone point me where I get wrong, or give me an idea on how to solve this?

thanks