Probability Shortcut: 3 Dices Rolled Together

Today I am going to share Probability shortcuts for problems based on Dice. Must Probability trick: When 2 Dices rolled together

Sum of dices when three dices are rolled together
If 1 appears on the first dice, 1 on the second dice and 1 on the third dice.
         
(1, 1, 1) = 1+1+1=3
The minimum sum with three dices rolled together = 3
If 6 appears on the first dice, 6 on the second dice and 6 on the third dice.
        
(6, 6, 6) = 6+6+6 =18
   
The maximum sum with three dices rolled together = 18
The sum could be 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.

  • What is the probability of getting a sum of 4 if three dices are rolled together.
        Solution:   
dice problems
            Total outcomes = 6x6x6 =216


Required probability = favorable case / total outcomes
                                                    = 3/216
                                                    = 1/72

  • What is the probability of getting a sum of 5 if you throw three dices together?
         Solution:
             
                                   
dice problems
                             Required Probability =  6/216 = 1/36





Now as you can see that it is a time consuming method, let us find a quick method to find the probability.


There are total 16 numbers (possible number of sums) and half of 16 is 8.

Counting 8 from both the sides we get 10 and 11 in the middle.

probability shortcut

Now we will construct the triangle which would help us to find the probability if three dices are rolled together.
probability trick
Memorizing the making of the above picture makes the 

calculation easier and faster.

  • What is the probability of getting a sum of 11 if three dices are rolled together?
         Solution:
                               From the table

                               Sum 11 = probability 27

                               Required probability = 27/216 =1/8 

  • What is the probability of getting a sum of 14 if three dices are rolled together?
         Solution:
                                     From the table

                                    Sum 14 = probability 15

                                    Required probability = 15/216

  • What is the probability of getting a sum of 11 or 9 if three dices are rolled together?
Solution:

From the table

Sum 11 = probability 27   and   sum 9 = probability 25

Since there is an ‘and’ so we will add

Required Probability = 27/216 +25/216 = 52/216

  • If 3 dices are rolled at the same time. What is the probability of all 3 dice showing even face values?
Solution:  Even faces means 2, 4, 6

There are 3 ways 2 can appear on in first go.

Similarly, there are 3 ways 4 can appear on in first go.
.
There are 3 ways 6 can appear on in first go.

So total number of ways: 3+3+3

Required probability = 9/216 =1/24

  • What is the probability of not getting 6 when 3 dice are rolled together?
Solution:

Probability of not getting 6 on the first die = 5/6

(As probability of getting 6 on first die is 1 so the probability of not getting 6 = 6-1=5)

And

Similarly, Probability of not getting 6 on the second die = 5/6

And

Probability of not getting 6 on the third die = 5/6

So the required probability = 5x5x5/216=125/216

Remember AND means multiply and OR means ADD.



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15 comments:

  1. wow......awesome trick sir hats off to you...................

    ReplyDelete
  2. Nandini Venkata SivaJuly 24, 2015 at 6:41 PM

    sir you gave similar shortcut lesson for probability but i lost that if available please send me the link sir

    ReplyDelete
  3. sir there are no 2015 vacancies when i click on apply link there is just 2014 and old vacancies

    ReplyDelete
  4. Thanks sir

    ReplyDelete
  5. Sir please provide me notes for alligation mixture

    ReplyDelete
  6. raman sir please help me

    just now i have filled ibps po5 application nd by mistake i selected muslim option(im hindu) as my religion .will it be a problem now ,i alredy paid fee what can i do now

    ReplyDelete
  7. 14th ka ans 1881 hoga na??

    ReplyDelete
  8. If 3 dices are rolled at the same time.
    What is the probability of all 3 dice showing even face values? - Sir, shouldn't the number of favourable cases be 3*3*3=27?

    ReplyDelete
  9. Hi friends anybody from Coimbatore tomorrow attend SBI po exam

    ReplyDelete
  10. Warrior ♍ ♪ ♫July 25, 2015 at 8:03 AM

    I am btech in civil engg...is this create any problem at the time of interview of bank po or bank clerk?

    ReplyDelete
  11. Sir I m facing difficulty in probability on cards questions.. Can u plzz help in this matter?

    ReplyDelete
  12. 14 ans is 2

    ReplyDelete

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