In a group of 50 students, 28 students enjoy playing video games and 18 students enjoy reading books. Among the students who play video games, 12 also enjoy reading books. If a student is selected at random from the group, what is the probability that the student enjoys either playing video games or reading books, or both?

Given two events  and  :

In Durban, phone numbers start with 031. After that there are seven more digits:

With these seven digits, there are many phone numbers possible in Durban. Here are two statements about one of these seven-digit phone numbers:

• The phone number includes the digit 7 at least once.

• The phone number includes the digits 2 and 5.

In a deck of playing cards, what is the relationship between the events 'drawing a spade' and 'drawing a heart'?

In a school, students were surveyed about their participation in extracurricular activities: Music, Sports, and Art. The results are as follows:

• 60 students participate in Music.
• 40 students participate in Sports.
• 35 students participate in Art.
• 25 students participate in both Music and Sports.
• 20 students participate in both Music and Art.
• 15 students participate in both Sports and Art.
• 10 students participate in all three activities.

How many students participate in at least one of the three activities?

Suppose we have two sets, and , which are in some sample space S. Furthermore, suppose we know the following probabilities about events from these sets:

A group of students is given the following event sets:

The sample space is