There is a 9/25 chance that two numbers will be added together such that their total exceeds their product.
The set of positive numbers are:
{1,2,3,4,5}
We have to independently select two numbers from these sets.
We are trying to determine the likelihood that the sum is larger than the product of the integers.
When one of the chosen numbers is 1, the total will always be greater than the product because:
1*1=1 & 1+1=2
1*2=2 & 1+2=3
1*3=3 & 1+3=4
1*4=4 & 1+4=5
1*5=5 & 1+5=6
and so on.
If we select 2 as both numbers then,
2*2=4 & 2+2=4
Here sum and the product are equal.
If not, the product will be bigger than the sum.
Now, the first stage is to evaluate the total number of two combinations that are feasible:
We have 5 alternatives for the first number and 5 alternatives for the second number.
The product of the number of possibilities in each scenario yields the total number of combinations:
C= 5*5=25
The following combinations have a sum that is greater than the product :
1 and 1
1 and 2
1 and 3
1 and 4
1 and 5
2 and 1
3 and 1
4 and 1
5 and 1
So, we get 9 combinations.
So, Probability,p=9/25
Therefore it is concluded that the probability is 9/25.
Learn more about probability here:
https://brainly.com/question/11234923
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