Ideal answer for: when three dice are thrown simultaneously then find the probability that sum of the digits is 16?
The probability of the sum of three dice being 16 is zero. The largest possible sum with three dice is 18 (6 + 6 + 6), so the sum of 16 is not achievable.
The probability of the sum of three dice being 16 is indeed zero. When three dice are thrown simultaneously, the maximum possible sum is 18 (when all dice show a 6). Since the sum of 16 is lower than the maximum achievable sum, it is not possible to obtain this specific sum.
To understand why the sum of 16 cannot be achieved, let’s consider all the possible combinations of dice rolls and their corresponding sums:
Dice 1
Dice 2
Dice 3
Sum
1
1
1
3
1
1
2
4
1
1
3
5
1
1
4
6
1
1
5
7
1
1
6
8
1
2
1
4
1
2
2
5
1
2
3
6
1
2
4
7
1
2
5
8
1
2
6
9
6
6
5
17
6
6
6
18
As seen in the table, there are no combinations that result in a sum of 16. Each cell represents a unique outcome of the dice roll, and it is evident that the sum of 16 is not present in the entire set of possible outcomes.
To further emphasize the impossibility of obtaining a sum of 16, consider the following quote by Albert Einstein, who was known for his mathematical prowess: “Insanity: doing the same thing over and over again and expecting different results.” In this case, rolling the three dice repeatedly will never yield a sum of 16 because it is simply not a possible outcome.
Interesting facts about dice rolling:
The standard dice used in most board games have six sides, numbered from 1 to 6.
Dice have been used for thousands of years, with the oldest known dice dating back over 5,000 years.
Dice games are prevalent in many cultures and have been used for both entertainment and divination purposes.
The probability of rolling a specific number on a fair six-sided die is 1 in 6, as each outcome is equally likely.
Dice are often used in probability and statistics to simulate random events and calculate odds.
In summary, the probability of the sum of three dice being 16 is zero because it is not a possible outcome given the maximum sum achievable with three dice being 18. This understanding can be supported by analyzing all the possible combinations of dice rolls. As Albert Einstein once said, expecting different results from repeating the same action is simply not rational.
You might discover the answer to “When three dice are thrown simultaneously then find the probability that sum of the digits is 16?” in this video
In this video, the speaker discusses the frequencies and probabilities when three dice are tossed. They explain the pattern of frequencies for different sums and calculate the frequencies for each sum. They also explain how to calculate the probabilities by dividing the favorable number of cases by the total number of outcomes. The speaker provides examples of different probabilities for various totals and discusses the probability of getting a total of at least 6 or a total between 9 and 12. They also explain how to calculate the probability of getting a total of at least 14. Overall, the video provides a comprehensive overview of the frequencies and probabilities when three dice are tossed.
Other responses to your inquiry
Probability of a sum of 16: 6/216 = 2.8%
2.8%
Probability of a sum of 16: 6/216 = 2.8%
Surely you will be interested in this
What is the probability of getting the sum 16 of three dice thrown simultaneously?
Answer to this: Probability that the sum is 16=6/6*6*6*=1/36.
How many ways can a sum of 16 be obtained with three dice?
Answer to this: Now add the individual numbers in each of the squares and you will get the numbers 3 through to 18. Now count all the squares which contain 16 and it should be six of them. Therefore the probability of getting a total of 16 will be 6/216 or 1/36.
What is the probability of getting a sum as 3 dice is thrown?
Probability of an event = {Number of favourable events } ⁄ {number of total events},or 216. The results are: Possibility of getting a sum of 3: 1/216 = 0.0046 × 100= 0.5% Possibility of getting a sum of 4: 3/216 = 0.0138 × 100 = 1.4%
What is the probability of getting a sum of 15 if 3 dice are thrown simultaneously 5?
If three dice are thrown simultaneously then probability of getting a sum of 15 is 5/108 .
What is the probability that two dice come up as the same number?
Answer: Therefore, we have a total of 15 x 6 = 90 ways that exactly two of the dice will come up as the same number. So the probability is 90/216 = 15/36 = 5/12. Was this answer helpful? Two dice rolled. Find the probability that the sum of number on two dice is greater than 8.
How to get sum of 15 when 3 dice are thrown simultaneously?
The answer is: When 3 dice are thrown simultaneously a sum of 15 can be obtained by the following combinations: (3,6,6),(4,5,6),(5,5,5) Let’s call the event of getting sum of 15 be E Then P (E)= (3 1
How to calculate dice roll probability?
Answer: Use this dice odds calculator to easily calculate any type of dice roll probability: sum of two dice, sum of multiple dice, getting a value greater than or less than on a given throw of N dice, and so on.
What is the probability of throwing a six with 6 tries?
This means that the probability of throwing at least one six with six tries is 1 – 0.3349 = 0.6651 or 66.51% giving odds of roughly 2/3. In effect, the multiplication in the denominator calculates the sample space whereas the multiplication in the numerator computes the number of unfavourable outcomes in the sample space.
How to get sum of 15 when 3 dice are thrown simultaneously?
When 3 dice are thrown simultaneously a sum of 15 can be obtained by the following combinations: (3,6,6),(4,5,6),(5,5,5) Let’s call the event of getting sum of 15 be E Then P (E)= (3 1
How do you calculate the probability of 2 dice?
As a response to this: For two dice, you should multiply the number of possible outcomes together to get 6 × 6 = 36. With subsequent dice, simply multiply the result by 6. If you use dice of a different shape, enter the number of their sides instead of 6. When rolling 2 dice, what is the probability of 7?
How many dice can you throw if you roll three dice?
Possibility for throwing six sided three dice will be 1, 2, 3, 4, 5 and 6 dots in each (three) dies. Three dice are roll at the same time, number of attainable outcome can be 6 3 = (6 × 6 × 6) = 216 because each die has 1 to 6 number on its dots. Now, let’s consider the possible sums from rolling three dice.
What is the probability of summing up to 7?
Answer will be: Let’s assume that a total of 7 occurs at least once. For 2 dice, there are 6 ways to throw the sum of 7 – (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). The total number of combinations for a pair of cube dice is 36. So the probability of summing up to 7 is 6/36 = 1/6 = 0.1666667.
