Example of ...
Example of beer' blind testing. Result is perfect for advertised product. One by the Common Company and three by the opponent' company. But it's three competing beers with change to 50% / 50% ...
Result = (100% / 4) * 0.5 * 4 = 50% for Common Company beer. Per 50% of people from each beer in the testing! It's 12.5% + 12.5% + 12.5% + 12.5% = 50%!
But if all of them will choose only one competing beer? Chance to it is 1 in 1,267,650,600,228, 229,401,496,703,205,376. But we are need more accuracy information, because we have more various results. Bernoulli experiment (?) is answer there.
It's all tests' result on the x axis, if I increase count of peoples who testing beer, result concentrate near of 50% more and more ...
Simple formulas
- Simultaneous events = A * B; (Logical AND);
- Independents events = A + B; (Logical OR);
Expected value
Expected value = ∑ k i * Reward i, where i ∈ [1;n] and n = count of tests;
Example №1: 52 cards and reward is between 1$ for deuce and 13$ for ace. I can get reward with Bid = 10$. Expected value = 364$ * 1/13 = 28$ ...
Games: 1,000;
Reward: $7,174;
Cost: $10,000;
Example №2: 52 cards and reward is 0.5$, 1$, 2$, 4$, 8$, 16$, 32$, 64$, 128$, 256$, 512$, 1024$, 2048$. Bid = 100$. Expected value = 4095.5$ * 1/13 = 315$ ... Second conditions is better!
Games: 1,000;
Reward: $319,777.5;
Cost: $100,000;
Tree of the variants
Invest into the project 1M$ ... I can choose between a few suggestions for get better ...
Different between tree of the variants and simple formula into the presentation full data for calculating. The tree possible to write as:
00 - no disease, negative test [ 0.3 * 0.6 * 0.9 * $25kk = $4,050,000 ]01 - no disease, positive test [ 0.3 * 0.6 * 0.1 * 0 = 0 ]10 - disease, negative test [ 0.3 * 0.4 * 0 = 0 ]11 - disease, positive test [ 0.7 * $250k = $175.000 ]Total: $4,225,000
Test of the disease for all adult Americans ... Also interesting how Bayes Theorem can help here, with repeated tests ...
00 - no disease, negative test [ 174,980,750 ]01 - no disease, positive test [ 17,500 ]10 - disease, negative test [ 0 ]11 - disease, positive test [ 1,750 peoples ]
Predictive analyze
Many examples how predictive analyze works into the real life ...