Question

A particular farm in New Jersey obtains much of its fall income from customers picking their own apples from its orchards. If it is beautifully sunny, the farm expects to bring in $2000 per weekend. If it is cold, the farmers expect only to bring in $1200. If it is actively raining, the income will drop to $500 per weekend. If the forecast for one of the weekends in October is 30% chance of rain and 20% chance of frost, what is the farm’s expected value of income for that weekend?

Answer 1

Expected value=

We have:

x: 2000 1200 500

p(x): 0.5 0.2 0.3

Since total Probability = 1, Probability of sunny = 1-probability of cold- Probability of rain

We have Probability of rain= 0.3, Probability of cold/frost=0.2

So Expected value= 2000*0.5 + 1200*0.2 + 500*0.3= $1390