Question

An individual is planning a trip to a baseball game for 16 people. Of the people planning to go to the baseball game, 8 can go on saturday and 12 can go on sunday, some of them can go on both days. How many people can only go to the game on saturday?

Answer 1

Answer: There are 4 people who only go to the game on Saturday.

Step-by-step explanation:

Let the number of people go on Saturday be n(A).

Let the number of people go on Sunday be n(B).

Since we have given that

n(A) = 8

n(B) = 12

n(A∪B)  = 16

According to rules, we get that

$n(A)+n(B)-n(A\cap B)=n(A\cup B)\\\\8+12-n(A\cap B)=16\\\\20-n(A\cap B)=16\\\\n(A\cap B)=20-16=4$

So, n(only go on Saturday) = n(only A) = n(A) - n(A∩B) = 8-4 = 4

Hence, there are 4 people who only go to the game on Saturday.