Using Multiplication

 

The bookstore/ice cream store illustrates the idea.  Represent the probability of getting the novel by entering the bookstore by 0.3 (there are 3 chances in 10 they will have it); likewise, represent the probability of getting an ice cream cone you will enjoy by entering the ice cream store as 0.9 (since it is almost certain they will have what you want).  Represent the value of finding the novel as $20 (think of this as what you are willing to pay for it).  Represent the value of enjoying the ice cream as $4 (again what you are willing to pay for it).  To get the expected benefit of an action, you multiple the number representing value by the number representing probability.  The expected benefit of entering the bookstore is $20 x .3 = $6.  The expected benefit of going to the ice cream store is $4 x .9 = $3.60

 

Using multiplication here captures the idea that the expected value of the action goes up (or down) as the value goes up (or down), and as the probability goes up (or down). 

 

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