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.

**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:**

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:**

*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.

Now we will
construct the triangle which would help us to find the probability if three
dices are rolled together.

*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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