Answer:
The percentage of the students scored an A in neither Math 101 nor English 101 is 55%
Step-by-step explanation:
* Lets study the meaning of or , and on probability
- The use of the word or means that you are calculating the probability
that either event A or event B happened
- Both events do not have to happen
- The use the word and, means that both event A and B have to happen
* The addition rules are:
# P(A or B) = P(A) + P(B) ⇒ mutually exclusive (events cannot happen
at the same time)
# P(A or B) = P(A) + P(B) - P(A and B) ⇒ non-mutually exclusive (if they
have at least one outcome in common)
- The union is written as A∪B or “A or B”.
- The Both is written as A∩B or “A and B”
* Lets solve the question
- There are 100 student enrolled in both math and English Exams
- 30% of them scored an A in Math
- 35% of them scored an A in English
- 20% of them scored an A in both
- To find the neither lets find either and then subtracted from the total
∵ P(A or B) = P(A) + P(B) - P(A and B)
∵ P(Math) = 30%
∵ P(English) = 35%
∵ P(Math ∩ English) = 20%
∴ P(Math ∪ English) = 30% + 35% - 20% = 45%
- To find the neither subtract either from the total
∵ The total of students who enrolled is 100
∴ The percentage of the students who enrolled is 100%
∴ The percentage of the students scored an A in neither Math nor
English = 100% - 45% = 55%
* The percentage of the students scored an A in neither Math 101 nor
English 101 is 55%
