Question

Asa buys a painting. There is a 26​% probability that the artist will become famous and the painting will be worth ​$1000. There is a 18​% probability that the painting will be destroyed by fire or some other disaster. If the painting is not destroyed and the artist does not become​ famous, it will be worth ​$500. The expected value of the painting is

Answer 1

Answer:

The expected value of the painting is $540.

Explanation:

We obtain the expected value of the painting by multiplying each possible outcome by the its associated probability and then summing these values.  

We can deduce the probability of the painting being worth $500 because we know that the probabilities have to sum 1 (or 100%). Therefore $x = 1-0.26-0.18=0.56$. The probability associated to the painting being worth $500 is 56%.

We have the following information:

Possible Value Associated Probability

$500                                 56%

$1000                                28%

$0                                      18%

Now we can calculate the expected value of the painting:

$EV = 500 *0.56+ 1000*0.26+ 0*0.18= 540$

Therefore the expected value of the painting is of $540.