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?

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%

b. x + 1

step-by-step explanation:

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step-by-step explanation: