Home

Red and Blue Marbles

1,460.3K Views

You have two jars, 50 red marbles and 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.

Share
vipin Scholar Asked on 26th July 2015 in Puzzles.
Add Comment
Cancel

    • 1 Answer(s)

    Given that the number of red and blue marbles are the same, we would tend to think that the odds are 50-50. we would try different combinations, such as 25 of each colored marble in a jar or putting all red marbles in one jar and all the blue in the other. we will still end up with a chance of 50%.

    So lets think of a better way to distribute the marbles. What if we put a single red marble in one jar and the rest of the marbles in the other jar? This way, we are guaranteed at least a 50% chance of getting a red marble (since one marble picked at random, doesn’t leave any room for choice).  Now that you have 49 red marbles left in the other jar, you have a nearly even chance of picking a red marble (49 out of 99).

    So let’s calculate the total probability.

    P( red marble ) = P( Jar 1 ) * P( red marble in Jar 1 ) + P( Jar 2 ) * P( red marble in Jar 2 )
    P( red marble ) = 0.5 * 1 + 0.5 * 49/99
    P( red marble ) = 0.7474

    Thus, we end up with ~75% chance of picking a red marble.

    Cancel
    ronret45 Expert Answered on 29th July 2015.
    Add Comment
    Cancel

    • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.

  • More puzzles to try-

  • Accenture Interview PuzzlesAdobe Interview PuzzlesAge RiddleAkbar Birbal PuzzlesAlgorithm PuzzlesAlphabet riddleAmazon Interview PuzzlesAnalytical MathematicsAptitude PuzzleBank PuzzlesBetting PuzzlesBrain TeasersCalendar PuzzlesCards PuzzlesChess Board PuzzleChess PuzzlesChristmas Puzzlecipher PuzzleCivil Services PuzzleClock time puzzleCognizant Interview PuzzlesCoins PuzzleComputational PuzzleconundrumCoronavirus PuzzleCoupondunia Interview PuzzleCritical Thinking Puzzledata analyticsData Structure Interview QuestionsDecode PuzzleDetective PuzzlesDice PuzzleDictionary Riddlesdifficult riddleEasy Math puzzlesEasy puzzlesEinstein puzzleEnglish RiddleFamily Tree Puzzlefamous puzzleFill in the blanks riddlesFinding Killer RiddlesFlipkart interview puzzlesFunny RiddlesGeneral KnowledgeGeographical PuzzleGoogle Code Jam 2014Google Interview PuzzlesGRE PuzzleHard Puzzle