I plan to have a food sale tomorrow on campus. If tomorrow is a sunny day, I plan to sale all of food and I can get an income of $200. If tomorrow is a heavy raining day, then I cannot sale any food, so I do not have any income. Assume I need spend $50 to prepare the food and the chance of raining tomorrow is 0.01. find my expected value of this event.

Expected value for the event = $148

Step-by-step explanation:

Expected value (EV) = Σ (Px*x)

Pr (rainy day) = 0.01

Px for rainy day = 0.01

Pr (sunny day) = 1-0.01 = 0.99

Px for sunny day = 0.99

If it's sunny, income = $200

Cost of preparation = $50

x for sunny day = 200-50 = 150

If it's rainy, income = $0

Cost of preparation = $50

x for sunny day = 0-50 = - 50

EV = Σ (Px * x)

EV = (0.99*150) + (0.01*-50)

EV = 148.5 + (-0.5) = 148.5-0.5

Expected value for the event = $148