offers hundreds of practice questions and video explanations. Go there now.

# Magoosh Brain Twister: A Trick Up His Sleeve?

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.

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

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

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

A… 5/54

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