Answer:
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
Step-by-step 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 )
=
= ![\frac{(1-p(pays|machine 1 is generous))*p(machine 1 is generous)}{[((1-0.10)*0.5)+ ((1-0.20)*0.5)]}](https://tex.z-dn.net/?f=%5Cfrac%7B%281-p%28pays%7Cmachine%201%20is%20generous%29%29%2Ap%28machine%201%20is%20generous%29%7D%7B%5B%28%281-0.10%29%2A0.5%29%2B%20%28%281-0.20%29%2A0.5%29%5D%7D)
=
= 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