Solution: 2017 Winter Final - 20

Author: Michiel Smid

Question

Consider a coin that comes up heads with probability 1/5 and comes up tails with probability 4/5. You flip this coin twice, independently of each other. For each heads, you win \$100. For each tails, you win \$50.
What is the expected value $\mathbb{E}(X)$ of $X$?

(a)

120

(b)

140

(c)

100

(d)

Solution

Let’s calculate the expected value of the each flip

$ \mathbb{E}(X) = 100 \cdot Pr(\text{Heads}) + 50 \cdot Pr(\text{Tails}) $

$ 100 \cdot \frac{1}{5} + 50 \cdot \frac{4}{5} $

$ = 20 + 40 $

$ = 60 $

Since we flip 2 coins, we double the expected value

$ \mathbb{E}(X) = 60 \cdot 2 $

$ \mathbb{E}(X) = 120 $