Question

In a casino in Black pool there are two slot machines: one that pays out 10 % of the time, and one that pays out 20 % of the time. Obviously, you would like to play on the machine that pays out 20 % of the time but you do not know which of the two machines is the more generous. You thus adopt the following strategy: you assume initially that the two machines are equally likely to be the generous machine. You then select one of the two machines at random and put a coin into it. Given that you lose that first bet estimate the probability that the machine you selected is the more generous of the two machines.

Answer 1

Answer:

(you will win in I) =.1

P(You will win in II) =0.2

P(you will lose in I) =0.9

P(you will lose in II) =0.8

P(I is generous) =x

P(II is generous) =x

P(you lose in I/ I is generous) =12.(0.9)x=.45x

P(you lose in II/ II is generous) =12.(0.8)x=0.4x

P(II is more generous/ you lose) =0.400.4+0.45=0.400.85

Part 1 does not require Bayes theorem. You want to see in total percentage of the population which strategy brings in more users.

1) 25% market share increase of 1.25(20%(30%))=7.5%

2) 15% market share increase of 1.15(10%(70%))=8.05%

Given the price is the same in both the city and suburb, I would choose a strategy that will bring more of the general population to use your product which is Suburbs strategy I.

(20%(30%)) = 6% are city dwellers that use your product

(10%(70%)) = 7% are suburbanites that use your product

Fraction of people who use your product are city dwellers =66+7=613