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Solution: 2013 Fall Midterm - 15

Author: Pat Morin

Question

If you flip a fair coin 4 times, what is the probability that the coin comes up heads exactly twice?

(a)

$1/{{4}\choose{2}}$

(b)

${{4}\choose{2}}/2^{4}$

(c)

$2^{4}/{{4}\choose{2}}$

(d)

$2/2^{4}$

Solution

Calculate the whole set

Let S be the set of all possible outcomes.

There are $ 2^4 = 16 $ possible outcomes.

$|S|=16$
Calculat size of event

Let A be the event that we land exactly 2 heads

We can choose 2 spots for the heads out of the 4 spots: $ \binom{4}{2} $

$|A| = \binom{4}{2}$
Profit

$\Pr(A) = \frac{|A|}{|S|}$

$\Pr(A) = \frac{\binom{4}{2}}{16}$