Question

Please give an example of when using the probability an event will occur is important to decision making.  Why?

Answer 1

=>probability can be used to aid the decision–making process.

=>For example, suppose we’re considering launching a new product on the market.

=>We conduct a pre–launch questionnaire and 86 out of the 100 questionnaire respondents say that they would buy our product if it was on the market.

=>We might translate this into the following probability statement:

                                        P(product successful) = 86 100 = 0.86,

=>which is quite good, and so surely we should launch the product. It looks promising! But . . . we should also consider the financial outcome of our situation.

=>For example, if the product is successful, we might make a reasonable profit, but if the product is not successful, we could stand to lose a lot more than we would gain under success (set–up costs, advertising, production costs etc), and such financial considerations could outweigh the high probability of success alone.

=>So, in real–life scenarios, not only do we use probability to aid the decision–making process, but we also take into account the financial implications of our decisions.

=>This is achieved by weighting the probability of different outcomes by their value, which is often financial.

=>The Expected Monetary Value (EMV ) of a single event is simply the probability of that event multiplied by the monetary value of that outcome

Another Example:

=> When rolling a die, if it’s a six you have to pay £5 but if it’s any other number you receive £2.50. Would you take on this bet?

              Probability                                      Financial outcome

              P(6) = 1/6                                           –£5

              P(Not a 6) = 5/6 £2.50

Therefore

EMV (Six) = 1 6 × −5.00 = −0.833

EMV (Not a Six) = 5 6 × 2.50 = 2.0833

and hence the expected monetary value of the bet is

EMV (Bet) = −0.833 + 2.083 = 1.25.

Therefore, in the long run, this would be a bet to take on as it has a positive expected monetary value.