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:
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:
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.
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?
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?
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)
Similarly, Probability of not getting 6 on the second die = 5/6
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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