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Magoosh Brain Twister: A Trick Up His Sleeve?

brain_twister

Welcome back, Magooshers! We hope that you enjoyed your holiday, and that you’re looking forward to a great 2015. What better way to start the year than with a brand new Brain Twister? Let’s get started.

A conjuror will roll one red, six-sided die in his right hand and two blue, six-sided dice. What is the probability that the number on the red die will be greater than the sum of the two blue dice?

(A) 5/54
(B) 5/108
(C) 11/216
(D) 7/36
(E) 5/18

 

Stumped? Check back on Thursday for the answer and explanation.

 

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15 Responses to Magoosh Brain Twister: A Trick Up His Sleeve?

  1. razi January 8, 2015 at 4:28 am #

    A

  2. Vida January 8, 2015 at 4:20 am #

    I’ve got a long solution for this question, and think the answer is 5/54.

  3. Harish T January 8, 2015 at 3:27 am #

    Answer A) Since, Favourable outcomes are
    R B B No
    3 1 1 1
    4 1,2 2,1 3 (Always we could add the previous total)
    5 1,2,3 3,2,1 6
    6 1,2,3,4 4,3,2,1 10

    Total fav outcomes is 20

    Probability = 20/6*6*6
    = 5/54

  4. Elizavetta January 8, 2015 at 1:32 am #

    A for sure, I wish I could attach my scratch paper to show the whole process

  5. Sanjay January 7, 2015 at 10:50 pm #

    C

  6. Qamar January 7, 2015 at 10:39 pm #

    Hello Chris
    According to my calculations answer is A – 5/54
    But it was time taking as I did it by listing technique. Kindly update us with right answer and time efficient solution.

  7. Oxana January 7, 2015 at 9:23 pm #

    two blues: 1 and 1 vs one red: 3,4,5,6 = Probability:1/6*1/6*4/6=4/6^3
    two blues: 1 and 2 vs one red: 4,5,6 = Probability:1/6*1/6*3/6*2=6/6^3
    two blues: 2 and 2 vs one red: 5,6 = Probability:1/6*1/6*2/6=2/6^3
    two blues: 1 and 3 vs one red: 5,6 = Probability:1/6*1/6*2/6*2=4/6^3
    two blues: 1 and 4 vs one red: 6 = Probability:1/6*1/6*1/6*2=2/6^3
    two blues: 2 and 3 vs one red: 6 = Probability:1/6*1/6*1/6*2=2/6^3
    We multiply by 2 when blues result in different values so they can be interchanged
    As we calculate probability for OR we have to sum six fractions which brings 20/6^3 or 5/54. A

  8. Saket January 7, 2015 at 8:56 pm #

    Assuming outcomes like (1,2) – (2,1) on blue dice to be same.

    Possibilities on blue dice (1,1) , (1,2) , (1,3) , (2,2) and, (2,3) ; total 5 cases.
    Corresponding possibilities on red dice = {3,4,5,6}, {4,5,6}, {5,6} and {6} so total of 4+3+2+1 = 10 cases.
    Total number of cases, on blue dice = (6C1x6C1)/2! , 2! for symmetrical cases like (1,2) – (2,1) , (2,3) – (3,2) and so on. on red dice = 6C1

    So, required probability = 10/( (6C1x6C1)/2!) x (6C1) ) = 5/54.

    Therefore, A is the answer.

  9. zahid ahmed January 7, 2015 at 8:53 am #

    A… 5/54

  10. hasan January 6, 2015 at 2:14 am #

    A

    • swaroop January 6, 2015 at 8:46 pm #

      D. As there are 2 blue dice, 6*6 gives the total number of possible outcomes = 36.
      Favorable outcomes, the Red dice can have a maximum value of 6. Rolling two blue dice and having there sum < 6, below are the possible values.
      1,1
      1,2
      1,3
      1,4
      2,1
      2,2
      2,3
      So there are 7 favorable outcomes.
      The answer should be D – 7/36

      Please let me know if this is incorrect.
      Your suggestions are welcome.
      Wish you happy and a prosperous new year 🙂

      Thanks,
      Swaroop

      • Oxana January 7, 2015 at 11:18 pm #

        You forgot about the red die: A conjuror will roll three dice. Though, mentioning of the right hand only for a red die does confuse (sorry Chris)))
        And more, when the values of blue dice are not equal (e.g., 2 and 3 as opposed to 1 and 1) you are supposed to double that probability.

      • Renato January 8, 2015 at 4:08 am #

        Accually, when you mentiones the possible outcomes, you forgot some:
        1,1
        1,2
        2,1
        1,3
        3,1
        1,4
        4,1
        2,2
        2,3
        3,2
        That gives us a total of 10 favorable outcomes. Therefore, the answer should be 10/36 or 5/18.

      • razi January 8, 2015 at 4:36 am #

        what about the probability of red one

        red blue1 blue2
        3 1 1 1/6*1/6*1/6
        4 1 1 1/6*1/6*1/6
        4 2 1
        4 1 2
        .
        .
        . ———————-
        the sum is 10/108=5/54
        the answer is A

      • Brainy January 8, 2015 at 7:05 am #

        You are forgetting 3 cases of 3,2 3,1 & 4,1. Also 10 cases when red dice is showing 3, 4 or 5 and is still larger than sum of 2 blue. For example, red is 3 and blue are both 1. Correct answer is A.


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