Solution
To get the maximum possible probability we can try different combinations like putting all the red marbles into JAR A and all the blue ones into JAR B. Then our probability will be
P(red marble): P(Jar 1) * P( red marble in Jar 1 ) + P( Jar 2 ) * P( red marble in Jar 2 ).
P(red marble): (½ * 1) + (½ * 0) = 0.5
As you can see from the above equation the probability that we are getting is 50%. You can try any other combinations like keeping 25 red marbles in jar A and 25 in jar B still you won’t get the maximum probability. So what’s the most optimal way to solve the problem?
What if you put all of the marbles in jar A keeping just one red marble in jar B? As only one marble will be chosen at random, you will always have at least a 50% chance of acquiring a red marble in this manner. There are 49 red marbles left in the other jar, giving you a nearly equal chance of choosing one (49 out of 99).
So the maximum probability will be:
P( red marble ) = P( Jar A ) * P( red marble in Jar A ) + P( Jar B ) * P( red marble in Jar B )
P( red marble ) = (½ * 1) + (½ * 49/99)
P( red marble ) = 74/99
P( red marble ) = 0.75 (rounded off to two decimal places)
We get 0.75 as our probability of getting the red marble which is the maximum possible probability we can achieve.
In this manner, you can solve the puzzle marbles in the jar.
Check out this problem - 8 Queens Problem
Frequently Asked Questions
What are some of the puzzles asked in an interview?
Most of the puzzles asked during interviews are designed to gauge your level of mental ability. Here are some common puzzles asked in an interview:
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Crossing the Bridge Puzzle
-
Marbles in the jar
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Heaven or Hell Puzzle
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Man Fell in Well Puzzle
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Birthday Cake Puzzle
Why do interviewers ask riddles?
Brain teaser questions are used in interviews to gauge a candidate's capacity for critical thinking, creativity, and problem-solving under pressure.
What are stress interviews?
An applicant is thrown off balance and placed in an unpleasant situation during a stress interview. It is intended to demonstrate how a candidate responds under pressure, manages stress, and resolves conflicts at work.
Conclusion
In this article, we have extensively discussed a very famous puzzle problem marbles in the jar asked in many interviews.
If you think this blog has helped you enhance your knowledge about the puzzle marbles in the jar and if you would like to learn more, check out our articles Camel and the Banana Puzzle, Tic Tac Toe Puzzle, Cheryl’s Birthday Puzzle, Mex Puzzle, and many more on our Website.
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