If you pick a number from between 1 and 25, it means that the sample space considered is 25 i.e. because there are 25 numbers.
In the first round, a number is picked between 1 and 25, this means that the probability of picking that one number from between 1 and 25 is:
[tex]\frac{1}{25}[/tex]
In the second round, you can pick 1 number from 25 numbers; making the probability of picking the second number:
[tex]\frac{1}{25}\text{ as well}[/tex]
Therefore if you pick 2 in the first round OR you pick 9 in the second round, that means:
[tex]\begin{gathered} P(A\text{ OR B) = P(A) + P(B)} \\ P(2\text{ OR 9) = P(2) or P(9)} \\ \\ We\text{ know that P(2) = P(9) = }\frac{1}{25} \\ \\ \text{Thus probability of getting a 2 or 9 is:} \\ P(2\text{ OR 9) = }\frac{1}{25}\text{ + }\frac{1}{25}=\text{ }\frac{2}{25} \end{gathered}[/tex]
Therefore the final answer is:
[tex]p(2\text{ OR 9) = }\frac{2}{25}[/tex]
