There are 2 bags, each can hold 50 balls; there are 50 black balls and 50 red balls. A bag is selected at random, and a ball is taken out from it. What is the maximum and minimum probability that the ball being taken out is red.

Question

There are 2 bags, each can hold 50 balls; there are  50 black balls and 50 red balls. A bag is selected at random, and a ball is taken out from it. What is the maximum and minimum probability that the ball being taken out is red.

shubhamsrg · Answer

let 1st bag have x red balls,
then it has 50-x black balls
also, 2nd bag then has 50-x red balls and x black balls

if x=0 or 50,
then our probability is maximum and minimum i.e. 0 and 1 ..

hartnn · Answer

sure ? where did u account for the probability of selecting a bag randomly. ?

shubhamsrg · Answer

hmm,,i assumed 1 bag has already been taken..

hartnn · Answer

nopes, its either 1/2,0 or 1/2,1/2

hartnn · Answer

i wanna know, which one, for sure....

shubhamsrg · Answer

after we select the bag, do we know how many balls are in there ?

shubhamsrg · Answer

i mean how many red balls*

hartnn · Answer

do we know? NO, can we find for max and min probab ?YES

hartnn · Answer

and i want to know the concept of what is min and max probability

shubhamsrg · Answer

then net probability i guess would be
(1/2 * x/50) + (1/2 * (50-x /50)
ans i guess is half? o.O missed something maybe ..

hartnn · Answer

u getting 1/2,1/2
right ?

hartnn · Answer

i was getting 1/2,0
some of my friends were also telling 1/2,1/2
so i got confused

shubhamsrg · Answer

hmm..

anonymous · Answer

Even I heard it first time....... what is max and min probability.

hartnn · Answer

i think max probab means a case in which the probab of selecting a red ball is max.
it will be when we select a bag with all red balls in it....so 1/2

anonymous · Answer

1 bags out of two. 1/2. 
The minimum probability you have said is quite a strange notion...if I don't choose at all, then it is 0.

anonymous · Answer

I agree with the above 
This is b/c we get the maximum probability when one bag is filled with 50 - black balls and the other with 50 red balls. Here the probability of selecting the bag with 50 - red balls is 1/2, and then the probability of selecting a red ball from this bag is 1. Thus the maximum probability will be 1/2* 1 = 1/2.

Again we get the minimum probability when one bag is filled with 50 - black balls and the other with 50 red balls, so that the probability of selecting the bag with 50 - black balls is 1/2. And from this bag the probability of selecting red ball is 0. Thus the minimum probability is 1/2 * 0 = 0.

Thus @hartnn u are correct since I get 1/2, 0.

hartnn · Answer

so there is no different concept like man or min probability...?

anonymous · Answer

I think so.

anonymous · Answer

Amazing....!!!!!
Isn't it??

hartnn · Answer

pretty much :)

anonymous · Answer

Even @hartnn  has question today..

Ha ha ha ha...

hartnn · Answer

lol! i am human, can't i have questions ? :P

anonymous · Answer

No....
Ha ha ha ha..