Question

In a casino in Atlantic City, 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.

1. What do I know?
2. What do I want to find out?
3. What do I expect the answer to be?
4. How do I go from what I know to what I want to find?
5. Is the answer consistent with what I expected?

Answer 1

probability = 0.5294

1) what i know is that there are two machines

2) the probability of choosing a machine that pays 20% of the time

3) expected answer = 0.5294 = 52.94%

4) buy making some assumptions while making the calculations

5) yes

Explanation:

Given data:

Number of machines = 2

Assuming probability of machine 2 = 20% = 0.20

Assuming probability of machine 1 = 10% = 0.10

since both machines have the ability to be generous i.e. pay 20% all the time

P( machine 1 is generous ) = P( machine 2 is generous ) = 0.5

this is since there are only two machines

hence find the probability that the chosen machine ( machine 1 ) is the generous machine after the player losses its first bet

P ( Machine 1 is generous | first bet lost )

=
`(P( machine 1 is generous n lost) )/(p(lost))` =
`((1-p(pays|machine 1 is generous))*p(machine 1 is generous))/([((1-0.10)*0.5)+ ((1-0.20)*0.5)])`

=
`((1-0.10)*0.5)/(0.85)` = 0.5294

This the probability that Machine 1 is generous after the player losses the first bet

1) what i know is that there are two machines

2) the probability of choosing a machine that pays 20% of the time

3) expected answer = 0.5294 = 52.94%

4) buy making some assumptions while making the calculations

5) yes