What is the probability of getting 1,2,3,4 when 5 dice are thrown and

In summary: B5b3UgY3JlYXRlcyBpbiB0aGlzIGlzIGNsZWFyLg==In summary, the probability of getting 1, 2, 3, 4 when 5 dice are thrown and one of them is not 5 is calculated using a multinomial distribution. The event we are looking for is any combination of 1, 2, 3, 4 without regard for order and the fifth dice can be any number except 5. This probability is found by adding the probabilities of different combinations of occupancy numbers in each of the 6 classes 1-6.
  • #1
MilenaMath
8
0
What is the probability of getting 1,2,3,4 when 5 dice are thrown and one of them is not 5.(the order of 1,2,3,4 doesn't matter)
I am really confused:
So I computed chances of getting correct numbers that is 1/6^4 times 5/6,then I multiply this by 4 times 5! Am I right?
 
Physics news on Phys.org
  • #2


MilenaMath said:
What is the probability of getting 1,2,3,4 when 5 dice are thrown and one of them is not 5.(the order of 1,2,3,4 doesn't matter)
Your question is unclear. Do you mean at least one each of 1, 2, 3, 4? Exactly one of each?
When you say one of them is not five, do you mean that a particular one is not five, that they are not all five, or that none of them are five?
 
  • #3


I need to get exactly 1,2,3,4(order doesn't matter) and the fifth dice can be whatever number but 5
 
  • #4


Sorry, still not clear. If you get 4, 2, 2, 3, 1, is that ok or not?
 
  • #5


MilenaMath said:
I need to get exactly 1,2,3,4(order doesn't matter) and the fifth dice can be whatever number but 5

From this description, it seems the event you want is
A = {1,1,2,3,4} or {1,2,2,3,4} or {1,2,3,3,4} or {1,2,3,4,4} or {1,2,3,4,6}, but without regard for order. Is that correct? If so, you can use a multinomial distribution to find
P{A} = p(2,1,1,1,0,0) + p(1,2,1,1,0,0) + ... + p(1,1,1,1,0,1), where these are the occupancy numbers in each of the 6 classes 1--6.

RGV
 

1. What is the probability of getting exactly 1, 2, 3, 4 when 5 dice are thrown?

The probability of getting exactly 1, 2, 3, 4 when 5 dice are thrown is 0.00032 or 0.032%. This can be calculated by taking the total number of ways to get 1, 2, 3, 4 (4) and dividing it by the total number of possible outcomes (1296).

2. Is it possible to get all 1, 2, 3, 4 when 5 dice are thrown?

Yes, it is possible to get all 1, 2, 3, 4 when 5 dice are thrown. The probability of this happening is 0.00016 or 0.016%. This can be calculated by taking the total number of ways to get all 1, 2, 3, 4 (1) and dividing it by the total number of possible outcomes (1296).

3. How many different combinations can be made when throwing 5 dice?

There are 1296 different combinations that can be made when throwing 5 dice. This can be calculated by taking the total number of possible outcomes for one die (6) and raising it to the power of the number of dice (5).

4. What is the probability of getting at least one 1, 2, 3, 4 when 5 dice are thrown?

The probability of getting at least one 1, 2, 3, 4 when 5 dice are thrown is 0.99074 or 99.074%. This can be calculated by subtracting the probability of not getting any 1, 2, 3, 4 from 1. The probability of not getting any 1, 2, 3, 4 is 0.00016 (calculated in question 2), so 1 - 0.00016 = 0.99074.

5. How does changing the number of dice thrown affect the probability of getting 1, 2, 3, 4?

As the number of dice thrown increases, the probability of getting 1, 2, 3, 4 also increases. This is because the more dice that are thrown, the more possible combinations there are to get 1, 2, 3, 4. For example, if 10 dice are thrown, the probability of getting 1, 2, 3, 4 is 0.000000000000000064 or 0.0000000000064%. This can be calculated by taking the total number of ways to get 1, 2, 3, 4 (4) and dividing it by the total number of possible outcomes (60,466,176).

Similar threads

  • Calculus and Beyond Homework Help
Replies
6
Views
5K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
Replies
8
Views
4K
Replies
2
Views
2K
Replies
4
Views
961
  • Set Theory, Logic, Probability, Statistics
2
Replies
41
Views
3K
  • Calculus and Beyond Homework Help
Replies
3
Views
734
  • Set Theory, Logic, Probability, Statistics
2
Replies
42
Views
4K
  • Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
Back
Top