Red Marbles, Blue Marbles

Problem: you have two jars, 50 red marbles, 50 blue marbles. 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. (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.

Solution

Chance! chance is easy if you know how to do the formula. we know that we have two choices to make. first we’ll pick a jar, and each jar will have a 1/2 chance of being picked. then we’ll pick a marble, and depending how we stack the marbles, we’ll have a (# of red marbles in jar)/(# of total marbles in jar) chance of getting a red one.

for example, say we put all the red marbles into JAR A and all the blue ones into JAR B. then our chances for picking a red one are:

1/2 chance we pick JAR A * 50/50 chance we pick a red marble
1/2 chance we pick JAR B * 0/50 chance we pick a red marble

do the math and you get 1/2 chance for a red marble from JAR A and a 0/2 chance for a red marble from JAR B. add ‘em up and you get the result = 1/2 chance for picking a red marble.

think about it for awhile and see if you can figure out the right combination. we had a 50/50 (guaranteed) chance in picking a red marble from JAR A, but we didn’t have to have 50 red marbles in there to guarantee those fantastic odds, did we? we could’ve just left 1 red marble in there and the odds are still 1/1. then we can take all those other marbles and throw them in JAR B to help the odds out there.

let’s look at those chances:

1/2 we pick JAR A * 1/1 we pick a red marble
1/2 we pick JAR B * 49/99 we pick a red marble

do the math and add them up to get 1/2 + 49/198 = 148/198, which is almost 3/4.

we can prove these are the best odds in a somewhat non-formal way as follows. our goal is to maximize the odds of picking a red marble. therefore we can subdivide this goal into maximizing the odds of picking a red marble in JAR A and maximizing the odds of picking a red marble in JAR B. if we do that, then we will have achieved our goal. it is true that by placing more red marbles into a jar we will increase the chances of picking a red marble. it is also true that by reducing the number of blue marbles in a jar we will increase the odds also. we’ve maximized the odds in JAR A since 1/1 is the maximum odds by reducing the number of blue marbles to 0 (the minimum). we’ve also maximized the number of red marbles in JAR B. if we added any more red marbles to JAR B we would have to take them out of JAR A which reduce the odds there to 0 (very bad). if we took any more blue ones out of JAR B we would have to put them inJAR A which reduce the odds there by 50% (very bad).

it wasn’t really a good proof, but QED anyway 😛

And The Phrase” The Sun Is On…!” Hurts..!

It is the day that i have awaited more than My 20th B’day. Ofcourse i dint worked that hard to deserve anything!

TORQUE_ A Technical Orchid……..Quest for Excellence is the event that i have wauted for.!The last event in the year 2011 in UCE…!

Initial hiccups couldn’t deter the determined organizers from conducting the event.!With a modest support from the department and a meagre amount of Rs.20,000/- funds!

I still wonder how these guys had managed such an event to fare far better than other events in University!

The very first day saw many fresh faces in department…

Enormous inflow of new waters flooded into old still waters.

With a big question mak on my face i continued to wonder ” Will it be a success..?”

There isn’t even a single instant from which i could learn nothing right from the startig of inagural function to the last word of Thanks gving speech of Valedictory!

Its alwaz irritating to sit in an audi hearing to some blah blah…of eminent speakers with all doors either closed or guarded by some self proclaimed coordinators.!

Somehow they got crowd for that Inagural!

I have managed to escape to stalls.!

I was participating in every torque…

This is my 3rd Torque and 3rd time i have been in stall!

When i was in 1st yr we dint celebrated even though we got some profits….!!

But as the time gre my mind started transforming and i found that celebration of every possible ocassion will be the essence of Engineering life.!

3 different teams in 3 Torques!

Ofcourse i(We) have started celebrating in 2nd yr!

The cricket fever which was feared of was perfectly battled!

Achievable target and dogged performance from Men In Blue and of course some luck of Mr.Cool MSD could have costed us dearly.!

But thanks to performers who kept the audience to glue to their chairs.!

U happened to be computer operator for that day’s culturals ” ROCK ON”

Very close to stage!

I Torque-10 It was ” MY Love Is Gone”

And In Torque-11 It was MJ’s ” DANGEROUS”

Everyone is going crazy of MJ these days….

I feel that MJ fever is still on even though MJ Departed.!

And the thing i came to know

and which has adrenalized my thoughts of organising a whole college event is That JNTU is under transformation!

I’m in the university since 3 yrs…

But i haven’t spotted A Jr Anchoring an Event…

Thanks to all enthusiastic jrs….

I expect their cooperation for whole college Techno-Cultural Fest!

And the other thing is A Boy and Girl from same class dancing together on same stage…!!

A welcomed sign for a world class university!

And the good news came by air in the midst of celebration that Men In Blue had edged Kangaroo’s out of CWC-11

Thunderous applause to MIB rocked the Whole university campus…!

Finally the show halted at 1:00 am

for the next few hours i have slept and when i woke up i found the Sun is Just on….

Another day of surprises is waiting!