Today I read a headline that said “75% Probability Apple Stays With AT&T”. That was based on: “"couldn’t find compelling evidence" that AT&T's contract with Apple ends this year. He gives it a 50% chance. Additionally, there's a 25% chance that AT&T would bid for -- and win -- another year of exclusivity. Add them up, you get 75%”.

Whenever somebody adds up probabilities, that sets off an alarm in my head. What if the analyst believed that there was a 60% probability that AT&T would get the new contract? Then the sum of the probabilities would be 110%. That’s a little more than absolute certainty, which never exists in the stock market.

The lesson here is to use a little, what I will call, “sense-itivity analysis”. Plug some plausible numbers in to make sure that the answer still passes a common sense test. We know that the probability must be 100% or less. In this case, it will certainly be less than 100%. So the result of 110% tells us that there is a math problem here. Doing a little “sense-itivity analysis” is a good idea in simulation models as well as the stock market.

For the record, the correct answer is 62.5%. I will let you work out the math.

## Thursday, February 4, 2010

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