Suppose there are three sports teams at school: Football Basketball Track If it is known that: 15 students play football. 12 play basketball. Ten run track. Eight play football and basketball. Four play football and run track. Four play basketball and run track. Three students play all three sports.

Suppose there are three sports teams at school:

1. Football
2. Basketball
3. Track

If it is known that:

• 15 students play football.
• 12 play basketball.
• Ten run track.
• Eight play football and basketball.
• Four play football and run track.
• Four play basketball and run track.
• Three students play all three sports.

Let’s set up a Venn Diagram that illustrates this scenario.

Joint Probability Venn Diagram

Now, let’s find the probability that a student plays football and basketball.

Probability Venn Diagram Additive Rule

Next, let’s determine the probability that a student plays football or basketball.

Probability Venn Diagram Multiplication Rule

And what is the probability a student runs track given that they are on the football team?