http://www.ck12.org Chapter 1. Independent and Dependent Events
We know that:
S={ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }
A={ 1 , 3 , 5 , 7 , 9 }
B={ 2 , 3 , 5 , 7 }
Notice that 3 of the prime numbers are part of both sets and are, therefore, in the overlapping part of the Venn
diagram. The numbers 4, 6, 8, and 10 are the numbers not part ofAorB, but they are still members of the sample
space.
A∩B={ 3 , 5 , 7 }
A∪B={ 1 , 2 , 3 , 5 , 7 , 9 }
Practice
1.ABCHigh School is debating whether or not to write a policy where all students must have uniforms and wear
them during school hours. In a survey, 45% of the students wanted uniforms, 35% did not, and 10% said
they did not mind a uniform and did not care if there was no uniform. Represent this information in a Venn
diagram.
2.ABCHigh School is debating whether or not to write a policy where all students must have uniforms and wear
them during school hours. In a survey, 45% of the students wanted uniforms, and 55% did not. Represent this
information in a Venn diagram.- For question 2, calculate the probability that a person selected at random fromABCHigh School will want the
school to have uniforms or will not want the school to have uniforms. - SupposeA={ 5 , 6 , 8 , 10 , 12 }andB={ 8 , 9 , 12 , 13 , 14 }. What isA∪B?
- SupposeA={ 1 , 7 , 13 , 17 , 21 , 25 }andB={ 7 , 14 , 21 , 28 , 35 , 42 }. What isA∩B?
- In Jason’s homeroom class, there are 11 students who have brown eyes, 5 students who are left-handed, and
3 students who have brown eyes and are left-handed. If there are a total of 26 students in Jason’s homeroom
class, how many of them neither have brown eyes nor are left-handed? - If eventAis randomly choosing a vowel from the letters of the alphabet, and eventBis randomly choosing
a consonant from the letters of the alphabet, do the ovals in the Venn diagram that represents this situation
overlap? Explain your answer. - Use the following Venn diagram to answer the question: