Two numbers are randomly selected on a number line numbered 1 through 9. The same number can be chosen twice. What is the probability that both numbers are greater than 6?

19

12

13

16

Question

Two numbers are randomly selected on a number line numbered 1 through 9. The same number can be chosen twice. What is the probability that both numbers are greater than 6?

19

12

13

16

owlcoffee · Answer

I'm not the best when it comes to probability but I think I can solve this.
First of all, we have to calculate al lthe possible outcomes, these being all the possible permutations of selections, these include the double-scenarios.
So, the possible outcomes are the ordered pairs we can form : $$(1,1)-(1,2)-(1,3)-...-(9,1)-(9,2)-...(9,9)$$
This means there are $9^2$ possible outcomes of this scenario BUT under the given conditions we will have to establish all the scenarios where the numbers will be greater than 6, this means from 6 to 9 there are three numbers and all the permutations possible are $3^2$. Let's call it the probability "P" and it will be composed by the division of the allowed permutations with the entirety of all the possible outcomes:
$$P=\frac{ 3^2 }{ 9^2 }$$
And you should be able to take over from here.

anonymous · Answer

thank you!