A mobile game uses two servers to handle matchmaking: one on the West Coast and one on the East Coast. The East Server has 50 free users and 20 premium, while the West server has 40 free users and 40 premium users. While the process for selecting the next user is random, there is a preference given for premium users: on each pick there is 60% than a premium user is selected and a 40% chance a free user is selected. What is the probability that the next player will be a free user from the East server?

Question

anonymous · Answer

Can someone help  me out here?

anonymous · Answer

Does anyone know how to this problem

phi · Answer

Prob of picking a free user from the east would be  50*0.4 / ( 60*0.6+90*0.4)

anonymous · Answer

How did you come up with those numbers

phi · Answer

they say  selecting the next user is random, so I assume that means the pool of users they are choosing from is 150 user  (70 from the east, 80 from the west)

if the choices were equally weighted, the chance of a free user from the east would be 
50/150

but the choices are not equal.  the premiums are weight 0.6 and the free are weighted 0.4
that means break the 150  into 60 premium and 90 free and weight them
to get  60*0.6 + 90*0.4

also, weight the 50 free up top, 50*0.4

we get
 50*0.4 / ( 60*0.6+90*0.4) = 20/(36+36) = 20/72 = 5/18

anonymous · Answer

When I did the second part of the problem it came out as .16

phi · Answer

what is the second part of the problem ?

anonymous · Answer

Never mind I type in the wrong numbers

anonymous · Answer

Thanks for your help