# Puzzle

We have 50 Red , 50 Blue Marbles and 2 jars. One of the jar is chosen at random and then one marble is chosen from that jar at random. How would we maximize the chance of choosing red marble ? What is the probability of choosing red marble ?. All 100 marbles should be placed in the jar.

# Solution

There are many combinations such that 100 marbles are in any one of the two jars. Now lets take a configuration 25 red and 25 blue marbles in one jar and the remaining 50 marbles in one jar.

P(choosing Red Marble)  = P(Jar 1) * P( Red Marble )  + P( Jar 2 ) * P( Red Marble)

= 0.5 * (25/50) + 0.5 *(25/50)

= 0.5

Let’s try a different combination

We can have one red marble in one jar and the remaining 99 marbles in another jar.

P(choosing Red Marble)  = P(Jar 1) * P( Red Marble )  + P( Jar 2 ) * P( Red Marble)

= 0.5 * 1+ 0.5 *(49/99)

= 0.5 + 0.24747474747

=0.747474

I hope this is the correct answer. I don’t have clear explanation how i arrived to one marble in the jar and remaining marbles in another jar. It was said to me by my friend Pandian