Question

Assume that with a 0.25 probability you are faced with a sick state where you get $20,000. Otherwise, you face a healthy state where you get $80,000

a. What is your expected income?

Answer 1

The expected income is calculated by multiplying each income outcome by its respective probability and adding the results together. In this case, with a 0.25 probability of earning $20,000 and a 0.75 probability of earning $80,000, the expected income is $65,000.

Step-by-step explanation:

To calculate the expected income, you need to multiply each outcome by its probability and sum these products. In the scenario provided, there is a 0.25 probability of being in a sick state with an income of $20,000, and a 0.75 probability (1 - 0.25) of being in a healthy state with an income of $80,000. The expected income can be calculated as follows:

• Expected income from sick state = Probability of sick state × Income in sick state = 0.25 × $20,000
• Expected income from healthy state = Probability of healthy state × Income in healthy state = 0.75 × $80,000

So the combined expected income is:

Expected income = Expected income from sick state + Expected income from healthy state

Expected income = (0.25 × $20,000) + (0.75 × $80,000)

Expected income = $5,000 + $60,000

Expected income = $65,000

Therefore, the expected income is $65,000.