SOLUTION: In a large school, it was found that 75% of students are taking a math class, 77% of student are taking an English class, and 57% of students are taking both. Find the probabili

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Question 1206043: In a large school, it was found that 75% of students are taking a math class, 77% of student are taking an English class, and 57% of students are taking both.
Find the probability that a randomly selected student is taking a math class or an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
Find the probability that a randomly selected student is taking neither a math class nor an English class. Write your answer as a decimal, and round to 2 decimal places if necessary.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

M = person takes Math
E = person takes English

Given info
P(M) = 0.75
P(E) = 0.77
P(M and E) = 0.57

Use the inclusion-exclusion principle to say:
P(M or E) = P(M)+P(E)-P(M and E)
P(M or E) = 0.75+0.77-0.57
P(M or E) = 0.95

Then,
P(neither M nor E) = 1 - P(M or E)
P(neither M nor E) = 1 - 0.95
P(neither M nor E) = 0.05