Okay, so this is a venn diagram. The number of students that do each activity will be displayed in the sections of the circles. The number 1 on the outside shows that that student is not involved in any of these activities, thus not being included in the circle. Think of it as the number of students being actual people in a diagram drawn like this one. There would be 11 people in the baseball circle, 7 people in the hockey circle, and 8 people in the soccer circle. However, these don't add up to the 18 that we originally added up to in the beginning. The circles overlap each other, showing the students that are in two activities instead of one, showing that they count for both categories. For example, there is a 2 in the section that is in between the soccer and hockey only sections. The very middle section is the one student that is involved in all three activities.
Now, we are looking for is the number of students that do baseball and soccer, but not hockey. You wouldn't look in the middle section, since that is the student that does all three. Look to the left, where the baseball and soccer circles coincide but the hockey circle never touches. This is the section of students that do baseball and soccer, but not hockey. That number is a 3.
Next, we answer the question of probability. The way you do this question is:
[tex] \frac{number of people that qualify}{total number of people} [/tex]
The number of people that qualify is 3, and the total number of people is 18. This is the probability because if you pick one person from the group of 18, 3 of them qualify, so you only have three possibilities of getting what the question asked for.
[Edit:]
Therefore, the answer is [tex] \frac{3}{18} [/tex]
I hope this helps!
