What is the expected value from rolling a 20-sided die?
Hint
The possible outcomes are the numbers 1 through 20, and the probability is equal for getting any particular result.
Answer
10.5
Example 2
You flip a coin 4 times. What is the expected value for the number of heads?
Hint
Be careful finding the probabilities. There is a 1/16 chance of getting 0 or 4 heads, 4/16 chance of getting 1 or 3 heads, and a 6/16 chance of getting 2 heads. List all the possible outcomes or use combinations to check this.
Answer
2 heads
Example 3
Every month, there is a raffle where each ticket costs $10, and the payout would be $3000. There are only 400 tickets available. Is this a good gamble?
Hint
You're guaranteed to spend $10, but there is a chance of winning $3000. What is the expected value?
Answer
No. The expected value is $7.50, while the cost of a ticket is $10.
Example 4
Which of these two investments offers a better return?
Company A: 40% chance of doubling your money; requires $10,000 initial investment.
Company B: 51% chance of receiving $25,000 in returns. Requires an initial investment of 15% of $25,000.
chance of winning $3000. What is the expected value?