# Decisions: probabilities and preferences

#### Alex_Bham

##### New Member
Hello everybody. I was wondering if anyone could help me with the following problem.

I need to decide between three options: a) spend my holiday in London; b) spend my holiday in Norwich; c) stay at home. My decision depends on two independent variables: 1. the chances that it will rain (expressed in percentages), 2. the strength of my preferences for each of three places (expressed in numbers).

As for the first variable, there is a 30% chance that it will rain in London, 5% that it will rain in Norwich and 10% for raining in my city. As for the second variable, my preference for going to London has the value of 9, for Norwich 6.7 and for staying at home 6.

What would be the formula for calculating the values from the two variables? Would simply the multiplication of the percentages with the whole numbers be a valid operation here?

Thanks for your help.
Alex

#### BGM

##### TS Contributor
One usual objective is to maximize the expected utility. For example if your second variable is utility (without rain?) already, now you need to also find out the utility under the raining scenario as well. Then calculate the expectation.

#### Alex_Bham

##### New Member
Hi BGM,

Thanks for your reply. I'm not sure I've got what you meant. Maybe I should have formulated my question in a slightly different way. Say if we instead of talking about rain we have the probabilities of meeting my old friend (so a positively instead of a negatively evaluated variable): then the probability for London would be 10%, for Norwich 30% and for staying home 20%. How could I in this case calculate the values of the preferences with these probabilities?