Calculating expected value can be tedious, especially when dealing with numerous probabilities and outcomes. But your trusty TI-84 calculator can significantly streamline this process. This guide will show you how to efficiently calculate expected value using your TI-84, eliminating guesswork and saving you valuable time. We'll cover the basics of expected value, different methods for calculation on your TI-84, and answer some frequently asked questions.
What is Expected Value?
Expected value (EV) represents the average outcome you'd expect over many repetitions of a random event. It's calculated by multiplying each possible outcome by its probability and then summing those products. For example, if you have a 50% chance of winning $10 and a 50% chance of winning $0, your expected value is (0.5 * $10) + (0.5 * $0) = $5. This means that on average, you'd expect to win $5 per game if you played many times.
Calculating Expected Value on Your TI-84: The List Method
This method is particularly useful when you have a longer list of outcomes and probabilities.
-
Enter the Outcomes: Press
STAT->EDIT. Enter your possible outcomes in L1. -
Enter the Probabilities: In L2, enter the corresponding probabilities for each outcome in L1. Ensure the probabilities add up to 1 (or 100%).
-
Calculate the Products: In L3, we'll calculate the product of each outcome and its probability. Use the formula L1 * L2. To do this, move your cursor to the top of L3, press
ENTER, then typeL1*L2and pressENTER. -
Sum the Products: Now, use the
sumfunction to add all the values in L3. Press2nd->STAT(LIST) ->MATH->5:sum(. Then typeL3and pressENTER. The displayed value is your expected value.
Example:
Let's say you have the following outcomes and probabilities:
| Outcome | Probability |
|---|---|
| $10 | 0.3 |
| $5 | 0.5 |
| $0 | 0.2 |
Following the steps above, your TI-84 will calculate the expected value as $6.
Calculating Expected Value on Your TI-84: The Direct Method (for simpler scenarios)
For scenarios with only a few outcomes and probabilities, you can directly input the calculation. This avoids using lists, but it's less efficient for more complex scenarios.
Simply input the calculation as follows: (probability1 * outcome1) + (probability2 * outcome2) + ... and press ENTER. Replace the placeholders with your actual values.
Example (using the same example as above):
(0.3*10) + (0.5*5) + (0.2*0) Press ENTER to get the expected value of $6.
How to calculate expected value with negative outcomes?
The process remains the same, regardless of whether outcomes are positive or negative. Simply input negative values as needed when entering outcomes into L1 (list method) or directly into the calculation (direct method).
What if my probabilities don't add up to 1?
If your probabilities don't sum to 1, you have an error in your data. Double-check your probability assignments to ensure they accurately reflect the likelihood of each outcome. The sum of probabilities for all possible outcomes must always equal 1.
Can I use this method for more than 3 outcomes?
Absolutely! Both methods can handle any number of outcomes and their corresponding probabilities. The list method is particularly recommended for scenarios with many outcomes to maintain organization and accuracy.
By mastering these techniques, you can confidently calculate expected values using your TI-84 calculator, enhancing your understanding of probability and decision-making. No more guessing – let your calculator do the heavy lifting!
