An urn contains 4 green, 6 blue and 10 yellow chips.
You pay $5 to draw a chip from the urn. Here are the rules of the game:
if you draw a green chip, the dealer returns you your bet and gives you an additional $5.
if you draw a blue chip, the dealer returns you your bet and gives you $1.
if you draw a yellow chip, the dealer keeps your $5.
What is the expected value of this game? (use formula for expected value of discrete distribution
How do I start solving this?
To find the expected value of a game, we need to calculate the weighted average of the possible outcomes. In this case, the outcomes are winning $10 (drawing a green chip), winning $1 (drawing a blue chip), and losing $5 (drawing a yellow chip).
To start solving this, we need to calculate the probabilities of each outcome. The total number of chips in the urn is 4 (green) + 6 (blue) + 10 (yellow) = 20.
The probability of drawing a green chip is 4/20 = 1/5.
The probability of drawing a blue chip is 6/20 = 3/10.
The probability of drawing a yellow chip is 10/20 = 1/2.
Now, we can calculate the expected value using the formula for expected value of a discrete distribution:
Expected value = (probability of outcome 1 * value of outcome 1) + (probability of outcome 2 * value of outcome 2) + ... + (probability of outcome n * value of outcome n)
In this case, the outcomes and their corresponding values are as follows:
Outcome 1: Winning $10 (green chip)
Outcome 2: Winning $1 (blue chip)
Outcome 3: Losing $5 (yellow chip)
Therefore, the expected value of this game can be calculated as:
Expected value = (1/5 * $10) + (3/10 * $1) + (1/2 * - $5)
Simplifying this equation will give you the expected value of the game.