Question

A carnival is being set up in your hometown. From experience, the carnival organizer knows that the amount of money he will bring in depends on the weather. If it is rainy, he will lose $5,000. If it is cloudy, he expects to earn $4,000. If it is sunny, he will bring in $12,000. The weather forecast shows that there is a 20% chance of rain and a 50% chance of sunny skies. Otherwise, it will be cloudy.A carnival is being set up in your hometown. From experience, the carnival organizer knows that the amount of money he will bring in depends on the weather. If it is rainy, he will lose $5,000. If it is cloudy, he expects to earn $4,000. If it is sunny, he will bring in $12,000. The weather forecast shows that there is a 20% chance of rain and a 50% chance of sunny skies. Otherwise, it will be cloudy.

Answer 1

$6,200

Explanation:

The question is to find the expected value.

We know the expected value of a scenario is the sum of the products of each probability of event and its profit or loss.

There are 3 probabilities in the scenario:

Rainy: 20% = 20/100 = 0.2

Sunny: 50% = 50/100 = 0.5

Cloudy: Rest, which is 100 - (50+20) = 100 - 70 = 30% = 30/100 = 0.3

Now, the gain and loss is:

Rainy: Lose 5000 means -5000

Cloudy: Gain 4000 means +4000

Sunny: Gain 12,000 means +12,000

Now, the expected value is:

Expected Value = (0.2)(-5000) + (0.5)(12000) + (0.3)(4000) = $6,200