It is known that among students 51% support candidate A for the student council,

ID: 2985200 • Letter: I

Question

It is known that among students 51% support candidate

A for the student

council, while only 49% support candidate B. In order

not to waste the time of too many

students, it was decided that instead of holding

general elections, n students will be selected

at random and the outcome of the elections will be

based on the majority vote among them

(the candidate receiving the most votes wins).

Suppose that n is small compared to the entire

student population, so that the votes of the n

selected students are essentially i.i.d.

1. Let Sn be the number of

students among the n who voted for candidate A. How is

distributed?

2. Write the event that candidate A wins the

elections in terms of Sn.

3. If n = 500, what is the probability that the

outcome of the elections is just (candidate A

wins)? Use Chebyshev's inequality.

4. Find a lower bound on n which will guarantee that

the outcome of the elections is just

with probability at least 97.5%?

1) Binomially Distributed

2) Sn > n/2

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