Calculate the probability for 2 different digits in 4 cells.

In summary, the probability for two different digits from the set {1,2,3,4} to appear in four cells is 3/8 or 37.5%. This can be calculated by first selecting the two digits to appear in the cells (in 4C2 ways) and then finding the possible arrangements for each case (both digits appearing twice, one digit appearing thrice and the other once). The total number of possible arrangements is then divided by the total number of possible combinations (4^4) to get the probability.
  • #1
yevi
66
0
The set S={1,2,3,4}, there are 4 cells.
What is the probability for 2 different digits (from S) to appear in 4 cells?
Example:

1,1,1,2 =>good
3,4,4,3 =>good
2,4,2,2 =>good

1,2,3,4 =>not good
1,2,3,3 =>not good
1,1,1,1=>not good
 
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  • #2
Count those where you have 1 of one element 3 of another, and then 2 each of two elements.
 
  • #3
Well, the 3 elements:

(4*3*2*3)/4^4

4 possibilities to choose first number, 3 possibilities to choose second number,
2 possibilities to choose third number and 3 possibilities to choose last number that has to be one of previous 3.

Is it right ?
 
  • #4
Doesn't seem at all right to me.
 
  • #5
This appears to be a home task. Since you have not informed that you got the solution, I am giving a broader hint.
1st select the two to appear in the cells--- in 4C2 ways.
For each of such choice find the no. of possible arrangements for the following cases.
1/ both of them is arising twice
2/ A specific no. of them arising thrice and the other once (and multiply this by 2,why?)
 

FAQ: Calculate the probability for 2 different digits in 4 cells.

What is the purpose of calculating the probability for 2 different digits in 4 cells?

The purpose of calculating the probability for 2 different digits in 4 cells is to determine the likelihood of a certain combination of numbers occurring within a set of four cells. This can be useful in various fields such as statistics, genetics, and gambling.

How do you calculate the probability for 2 different digits in 4 cells?

To calculate the probability for 2 different digits in 4 cells, you first need to determine the total number of possible combinations of digits in 4 cells. This can be done using the formula nCr = n! / (r! * (n-r)!), where n is the total number of digits and r is the number of cells. Then, calculate the number of combinations that meet the criteria (such as 2 different digits) and divide it by the total number of possible combinations.

Can the probability for 2 different digits in 4 cells be greater than 1?

No, the probability for any event cannot be greater than 1. A probability of 1 means the event is certain to occur, while a probability of 0 means it is impossible to occur. The probability for 2 different digits in 4 cells is always less than or equal to 1.

How can the probability for 2 different digits in 4 cells be used in genetics?

In genetics, the probability for 2 different digits in 4 cells can be used to determine the likelihood of specific genetic traits being passed down from parents to offspring. This can help in predicting the inheritance of diseases or physical characteristics.

Are there any real-world applications for calculating the probability for 2 different digits in 4 cells?

Yes, there are many real-world applications for calculating the probability for 2 different digits in 4 cells. For example, it can be used in gambling to determine the likelihood of certain outcomes in games of chance. It can also be used in quality control to assess the likelihood of a product meeting certain specifications based on its components.

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