SOLUTION: The probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 69% while 28% require a develo

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Question 1168149: The probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 69% while 28% require a developmental math course and 21% require a developmental English course.
Find the probability that a first year student requires both a development math course and a developmental English course.
Answer by ikleyn(52811) About Me  (Show Source):
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From the condition,

    P(English OR Math) = 100% - 69% = 31%.



From the basic formula of the Elementary Probability theory

    P(English OR Math) = P(English) + P(Math) - P(English AND Math).



Substitute all known / given values into this formula

    31% = 21% + 28% - P(English AND Math).



From this equation, find P(English AND Math)

    P(English AND Math) = 21% + 28% - 31% = 18%.    ANSWER

Solved.