Question

150 students in a tenth grade high school class take a survey about which video game consoles they own. 60 students answer that one of their consoles is a Playstation, 50 answer that one of their consoles is an Xbox. Out of these, there are 20 who have both systems.

Answer 1

Given:

Total Number of students surveyed = 150

Number of students having Playstation = 60

Number of students having XBox = 50

Number of students having both = 20

To Find:

The number of students having non of the console.

Solution:

Let A represent the event that a student has a playstation.

Let B represent the event that a student has a Xbox.

• Event that a student has both = A∩B
• Event that a student has either = n(A∪B)
• Even that a student has neither = Total students - n(A∪B)

Given,

• n(A) = 60
• n(B) = 50
• n(A∩B) =20
• n(A∪B) = n(A) + n(B) - n(A∩B)
• n(A∪B) = 60 + 50 - 20 = 90

Therefore the number of students having neither = 150 - 90 = 60