5) The probability that a college freshman takes a math class the first semester is 0.75. The probability tha

5) The probability that a college freshman takes a math class the first semester is 0.75. The probability that a freshman takes an English class the first semester is 0.7. The probability that the student takes both classes the first semester is 0.6.


a) Find the probability that the student takes Math or English in the first semester.


b) Find the probability that the student takes neither class in the first semester.


c) Are the events that a student takes a Math class and the event that a student takes an English class independent events? Show work to prove your answer.





6) 76 college students are surveyed about their favorite pizza topping and the following results are found:


Anchovies Mushrooms Onions Pepperoni


Freshmen 4 12 8 14


Sophomores 4 11 6 17





a) What is the probability that a randomly selected student has onions as their favorite topping?


b) If a sophomore is selected what is the probability that their favorite topping is pepperoni?


c) What is the probability that a randomly selected student is a freshman and their favorite topping is anchovies?


d) Given that you choose one person and their favorite topping is mushrooms or onions then what is the probability that the person is a sophomore?

5) The probability that a college freshman takes a math class the first semester is 0.75. The probability tha
For any two events A and B





P( A U B ) = P( A ) + P( B ) - P( A ∩ B )





Let E be the event the student takes and English class


Let M be the event the student takes a Math class.


Let ~E be the event the student does not take an English class


Let ~M be the event the student does not take a math class





P(E) = 0.7


P(M) = 0.75


P( E ∩ M ) = 0.60


Let ~E be the event the su








a) find P( E U M ) = 0.7 +0.75 - 0.6 = 0.85


b) find P(~E ∩ ~M)





use DeMorgan's Laws


~(A U B) = ~A ∩ ~B


~(A ∩ B) = ~A U ~B





P(~E ∩ ~M) = P( ~(E U M) ) = 1 - P( E U M) = 1 -0.85 = 0.15





c) for two events to be independent


P( A | B ) = P( A ∩ B ) / P( B ) = P(A)





P(E | M) = P(E ∩ M) / P(M) = 0.60 / 0.75 = 0.80 ≠ P(E) = 0.7





the events are not independent.





== -- == -- == -- == -- ==





6)





there are a total of 38 freshmen


total of 38 sophomores





total anchovies = 8


total mushrooms = 23


total onions = 14


total pepperoni = 31





a) P(onions) = 14/76


b) P(pepperoni ∩ sophomore) = 17/76


c) P(anchovies ∩ freshman ) = 4/76


d) find P( sophmore | (mushroom or onions) )





= P( Sophomore ∩ (mushrooms or onions) ) / P(mush or onions)





= ( 17/76 ) / (37/76)


= 17/37
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