Q:

Among 100 students who enrolled in both Math 101 and English 101, 30% of the students scored an A in Math 101, 35% of the students scored an A in English 101, and 20% of the students scored an A in both Math 101 and English 101. What percentage of the students scored an A in neither Math 101 nor English 101?

Accepted Solution

A:
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%