Question

Please include the steps on how to solve for P, I cannot find any instructions from any other resources, thank you.

1. Given IS = 290, IH = 1,490, E(I) = 1,280, solve for P (probability of being sick)

Answer 1

Solution:

Income when person is sick, IS = $290

Income when person is healthy, IH = $1490

Expected income, E(I) = income when person is sick*probability of being sick + income when person is healthy*probability of being healthy

Of course, probability of being healthy = 1 - probability of being sick

So, E(I) = 1280 = 290*P + 1490*(1 - P)

1280 = 290*P + 1490 - 1490*P

(1490 - 290)*P = 1490 - 1280

1200*P = 210

So, P = 210/1200 = 0.175

The probability of being sick is 0.175