Question

~~You have three options for the evening.

1. You could watch some sitcoms on TV that you are certain to enjoy and that will provide you with a pleasure rating of 4.

2. You could go to a movie that is supposed to be good. You would enjoy the movie with probability 0.5; if you enjoy it, it will provide you with a relative pleasure rating of 11, but if you don't enjoy it, it will provide you with a negative rating of -2.

3. You could go on a date. With probability 0.3 you will experience a pleasure rating of 21, and a probability of 0.7 the date will provide a negative rating of -2.

Discuss what you would do.
What are the expected values of pleasure for these individual activities?
TV expected value = ?
Movie expected value = ?
Date expected value = ?
Based on your numerical results, which option would you choose for the evening?

Answer 1

TV expected rating: 4 because of certainty of enjoyment.

Movie: 0.5 probability of 11; 0.5 probability of -2.

Date: 0.3 probability of 21; 0.7 probability of -2.

The only guaranteed rating is TV.
 

In a 100 evenings: 100 evenings' TV would earn 400; 100 evenings at the movies would earn 0.5*100*11-0.5*100*2=550-100=450; 100 dates would earn 0.3*100*21-0.7*100*2=630-140=490. Total=400+450+490=1340. The expected ratings: TV=400/1340=0.2985; movie: 450/1340=0.3358; date: 490/1340=0.3657. The relative  probabilities seem to indicate on balance that a date is more likely than the other two options to be the best option. But the only guarantee of enjoyment and a guaranteed rating of 4 is the TV option.