A favorite sports poll of 30 teenagers shows that 18 like soccer, 9 like baseball and 10 like ice hockey. Three teenagers like all three sports, 3 like only soccer and baseball, 4 like only hockey and soccer, and 3 like only hockey. How many teenagers do not like any of these sports
draw a Venn diagram, fill in the given data and all mysteries will become clear to you
Draw a Venn diagram. You will see that 28 like some sport. So, 2 like none of them.
A favorite sports poll of 30 teenagers shows that 18 like soccer, 9 like baseball and 10 like ice hockey. Three teenagers like all three sports, 3 like only soccer and baseball, 4 like only hockey and soccer, and 3 like only hockey. How many teenagers do not like any of these sports?
To find out how many teenagers do not like any of these sports, we need to analyze the given information.
First, we know the total number of teenagers surveyed is 30.
Next, we can break down the information about the number of teenagers who like each sport using a Venn diagram.
Let's start by drawing a Venn diagram with three circles representing soccer, baseball, and ice hockey.
The circle for soccer will represent the number of teenagers who like soccer, the circle for baseball will represent the number of teenagers who like baseball, and the circle for ice hockey will represent the number of teenagers who like ice hockey.
Now, let's fill in the information we have:
- We are told that three teenagers like all three sports, so we can place the number 3 in the region where all three circles overlap.
- We are also told that three teenagers like only soccer and baseball, so we can place the number 3 in the region where the soccer and baseball circles overlap, but not ice hockey.
- Similarly, four teenagers like only hockey and soccer, so we can place the number 4 in the region where the soccer and ice hockey circles overlap, but not baseball.
- Finally, we are told that three teenagers like only ice hockey. We can place the number 3 in the region where only the ice hockey circle is filled.
Now, let's calculate the remaining numbers:
- To find the number of teenagers who like only soccer, we subtract the numbers we have already placed from the total number of teenagers who like soccer: 18 - (3 + 3 + 4) = 8.
- Similarly, the number of teenagers who like only baseball is 9 - (3 + 3) = 3.
To calculate the number of teenagers who do not like any of these sports, we subtract the total number of teenagers who like at least one sport from the total number of teenagers surveyed:
Total number of teenagers who like at least one sport = number of teenagers who like only soccer + number of teenagers who like only baseball + number of teenagers who like only ice hockey + number of teenagers who like all three sports
= 8 + 3 + 3 + 3 = 17.
Number of teenagers who do not like any of these sports = Total number of teenagers surveyed - Total number of teenagers who like at least one sport
= 30 - 17 = 13.
Therefore, there are 13 teenagers who do not like any of these sports.