Solution: 2019 Winter Final - 11

Author: Michiel Smid

Question

You flip a fair coin 6 times; the flips are independent of each other. What is the probability that in these 6 coin flips, the coin comes up heads exactly 3 times?

(a)

4/16

(b)

6/16

(c)

5/16

(d)

3/16

Solution

Find S

Let S be the sample space of all possible outcomes of flipping a coin 6 times.

$|S| = 2^6 = 64$
Find A

Let A be the event that the coin comes up heads exactly 3 times.

We choose 3 of the 6 flips to be heads: $\binom{6}{3} = 20$

The remaining 3 flips must be tails: 1
Find $ \Pr(A) $

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

$ \Pr(A) = \frac{20}{64} = \frac{5}{16} $