The equation you provided can be interpreted as a method to calculate the expected value of a situation where there are two possible outcomes. Let's break it down:

Equation:

\text{(expected value} \times \text{probability)} + \text{(expected value 2} \times (1 - \text{probability}))}

Explanation:

1. Expected Value: This is the average value you would expect to get if you could repeat the situation many times. In this case, you have two possible outcomes, each with its own expected value:

   • Expected Value 1: The expected value associated with the first outcome.
   • Expected Value 2: The expected value associated with the second outcome.

2. Probability: This is the likelihood that the first outcome will occur. It ranges between 0 (impossible) and 1 (certain).

3. 1 - Probability: This represents the likelihood that the second outcome will occur. Since the total probability of all outcomes must equal 1, if the probability of the first outcome is $p$, the probability of the second outcome is $1 - p$.

How the Equation Works:

• The term $(\text{expected value} \times \text{probability})$ calculates the contribution to the overall expected value from the first outcome. It weights the expected value of this outcome by the likelihood of it happening.

• The term $(\text{expected value 2} \times (1 - \text{probability}))$ does the same for the second outcome.

• Adding these two terms together gives the total expected value for the situation, taking into account the probabilities of both outcomes.

Example:

Suppose you are flipping a coin, and you win $10 if heads comes up and $5 if tails comes up. The probability of heads is 0.5 (since it's a fair coin). The equation to find the expected value of your winnings would be:

$\text{Expected Value} = (10 \times 0.5) + (5 \times (1 - 0.5)) = 5 + 2.5 = 7.5$

So, the expected value of your winnings from the coin flip is $7.5.

Would you like to dive deeper into any part of this explanation?

Related Questions:

1. How does the concept of expected value apply in decision-making?
2. What is the difference between expected value and expected utility?
3. How would the equation change if there were more than two outcomes?
4. Can expected value be applied in situations involving continuous variables?
5. How do probabilities affect the expected value in risk assessment?

Tip:

When calculating expected value, always ensure that the sum of the probabilities of all possible outcomes equals 1.