Q no: 1 You are selling a product in an area where 30 % of the people live in the city and the rest live in the suburbs. Currently 20 % of the city dwellers use your product and 10 % of the suburbanites use your product. You are presented with two new sales strategies the first will increase your market share in the suburbs to 15 %. The second will increase your market share in the city to 25 %. Which strategy should you adopt? What percentage of the people who own your product are city dwellers before your new sales drive?
Q2: In a casino in Blackpool 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 loose that first bet estimate the probability that the machine you selected is the more generous of the two machines?
I need solutions of these two questions by using Bayer's Theorem .
P(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) $= \frac{1}{2}.(0.9)x =.45x$
P(you lose in II/ II is generous) $= \frac{1}{2}.(0.8)x = 0.4x$
P(II is more generous/ you lose) $= \frac{0.40}{0.4+0.45} = \frac{0.40}{0.85}$
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 $= \frac{6}{6+7} =\frac{6}{13}$