To determine the probability that Marlon's friend will think of the number 9 when asked to pick a number from 5 to 11, let's follow a step-by-step solution:
1. Identify the Range of Numbers:
Marlon's friend can think of any number between 5 and 11, inclusive. This means the possible numbers are 5, 6, 7, 8, 9, 10, and 11.
2. Count the Total Number of Possible Outcomes:
We need to count how many numbers are in this range:
[tex]\[
5, 6, 7, 8, 9, 10, 11
\][/tex]
There are 7 numbers in total, so the total number of possible outcomes is 7.
3. Identify the Favorable Outcome:
The favorable outcome is the specific event that Marlon’s friend thinks of the number 9. Since we are only interested in the number 9, there is 1 favorable outcome.
4. Calculate the Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the probability [tex]\( P \)[/tex] is:
[tex]\[
P(\text{thinking of } 9) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{7}
\][/tex]
Thus, the probability that Marlon's friend will think of the number 9 is [tex]\(\frac{1}{7}\)[/tex]. Therefore, the correct choice is:
[tex]\[
\boxed{\frac{1}{7}}
\][/tex]
