You have two jars 50 red marbles and 50 blue marbles.
If you have 2 jars with 1000 blue marbles.
For jar 1 we have that.
Each jar can hold 100 marbles.
600 red and 400 white jar 2.
How would you maximize the chance of drawing a red marble.
We calculate the probability of obtaining a red a blue and a green marbles.
One of the jars is chosen at random and then one marble will be chosen from that jar at random.
Seems tricky at first right.
Interview candidate on jan 2 2013.
In other words you get to take 2 measurements or comparisons here.
All 100 marbles should be placed in the jars.
You have 3 jars containing marbles as follows.
Jar 1 300 red and 700 white.
3 you are allowed to use set the scale twice in total.
You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar you maximize the chances that it will be red.
For jar 2 we have that.
When picking you ll first randomly pick a jar and then randomly pick a marble out of that jar you can arrange the marbles however you like but each marble must be in a jar.
One of the jars will be chosen at random.
Then 1 marble will be withdrawn from that jar at random.
Jar 3 500 green and 500 white.
Now we want to place these 100 marbles in 2 jars to maximize the probability of red marble pick.
4 each bucket has enough room for multiple marbles.
10 green and 990 white.
You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar you maximize the chances that it will be red.
I don t agree with your solution.
You can decide how many and what marbles to be placed in each of the jars.
You must place all 100 marbles in the jars.
You have two jars 50 red marbles and 50 blue marbles.
Fifty of the marbles are red and fifty are blue.
900 blue and 100 white jar 3.
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What is the probability of doing so.
You have two jars and hundred marbles.
We have 2 jars and not 1.
If you still don t believe it go buy 2000 marbles and try it yourself.
Total 100 marbles out of which 50 are red and 50 are blue coloured.
As long as you have the same number of marbles in each side the heavy marble has just enough weight to tip the scale to its side.
Additionally the other jar will have 1000 x blue marbles in it.
You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar you maximize the chances that it will be red.
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When picking you ll first randomly pick a jar and then randomly pick a marble out of that jar.
When picking you ll first randomly pick a jar and then randomly pick a marble out of that jar.
You can arrange the marbles however you like but each marble must be in.
You have 50 red marbles 50 blue marbles and 2 jars.
You have three jars containing marbles as follows.
Jar 2 20 blue and 980 white.
So the ratio of blue to red in one jar is the inverse of the other.