Question

You are playing a game where you flip a coin. If it lands heads, you win $4, but if it lands tails, you lose $2.
What is the expected value of this game?
A.$1.00
B.$0.50
C.$0.00
D.-$0.50

Answer 1

To calculate the expected value of the game, we need to consider the possible outcomes, their probabilities, and their associated values.

There are two outcomes when flipping the coin:
1. Heads: You win $4
2. Tails: You lose $2

The probability of each outcome is:
- Probability of heads (win $4): \( P(H) = \frac{1}{2} \)
- Probability of tails (lose $2): \( P(T) = \frac{1}{2} \)

Now, we can calculate the expected value (EV) using the formula:

\[
EV = (P(H) \cdot \text{Value of heads}) + (P(T) \cdot \text{Value of tails})
\]

Substituting in the values:

\[
EV = \left( \frac{1}{2} \cdot 4 \right) + \left( \frac{1}{2} \cdot (-2) \right)
\]

Calculating each term:

1. For heads:

\[
\frac{1}{2} \cdot 4 = 2
\]

2. For tails:

\[
\frac{1}{2} \cdot (-2) = -1
\]

Now combine these results:

\[
EV = 2 - 1 = 1
\]

So, the expected value of the game is **$1.00**.

The correct answer is **A. $1.00**.