minkwe wrote:Justo, please do yourself a favor and take 5 minutes to read my description of the example again. You are clearly not engaging with it, but with some other erroneous misinterpretation.
Here it is again step by step:
1.Say a smart mathematician knows a thing or two about coins and probability theory, so he confidently derives and writes down an equality relationship that holds for all coins based on the assumptions that (1) coins have 2 sides, (2) Probabilities of mutually exclusive possibilities must add up to exactly 1. This relationship applies to all coins, no matter how biased
, where (H=head or T=tail).
Do you have any issues with this part
No, I do not.
minkwe wrote:2. He's not an experimentalist, thus to test this relationship in the lab, contacts his friend who has designed a coin-reading machine. The machine works by accepting one of two settings (H=head or T=tail). A coin is tossed into an opening above the machine, causing a bell to ring if the coin comes up the same side as the setting.
Together, they perform an experiment, with the machine set to H. After 50 tosses, they get 40 rings. . They repeat the experiment with the setting at T and after 50 tosses, they get 35 rings.
What about this part, Amy objections?
Yes, first you did not answer a previous question. I asked if your reading machine influences the result of the coin toss. I assume that it does not, but since the results of your coin tosses contradict your assumption (2) we have doubts. I repeat that is why Richard Gill told you that you have to use probabilities conditional on the settings. He assumed that the machine setting biases the result.
The results or your experiments are P(H)=40/50=0.8 and P(T)=35/50=0.7 giving
, hence contradicticting your assumption (2).