Class has 28 students. 23 like basketball. Also, 15 like baseball. 12 like both. How many students do not like either.
do it with Venn diagrams
Draw two intersecting circles, call one basketball, the other baseball.
put 12 in the intersection.
Look at the basketball circle, 12 of the 23 that like it have already been placed in that circle, put the remainder of 11 in the open part of basketball.
In the same way put 3 in the open part of baseball.
Adding up the 3 numbers in the circles, 11 + 12 + 3 = 26
But there were 28 students, so 2 are not in either circle.
so 2 don't like either.
12÷2=6
23-6=17basketball
15-6=9baseball
27+9=26
28-26=2
To find the number of students who do not like either basketball or baseball, we need to subtract the number of students who like either or both sports from the total number of students in the class.
1. Start with the total number of students in the class: 28.
2. Subtract the number of students who like basketball: 28 - 23 = 5.
3. Subtract the number of students who like baseball: 5 - 15 = -10.
Since we have a negative number, it means that we made a mistake in the calculations. The negative result suggests that there is some overlap or duplication in the numbers provided.
Given that 23 students like basketball and 15 students like baseball, but 12 students like both, we need to consider the overlap.
To calculate the number of students who do not like either basketball or baseball, we can use the principle of inclusion-exclusion:
1. Start with the total number of students in the class: 28.
2. Subtract the number of students who like basketball: 28 - 23 = 5.
3. Subtract the number of students who like baseball: 5 - 15 = -10.
4. Add the number of students who like both sports to correct the overlap: -10 + 12 = 2.
Based on this calculation, there are 2 students who do not like either basketball or baseball.