SOLUTION: Let A be the event that a randomly selected college student has taken a statistics course and let B be the event that the same student has taken a chemistry course. Suppose P(A)=0.

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Question 1160500: Let A be the event that a randomly selected college student has taken a statistics course and let B be the event that the same student has taken a chemistry course. Suppose P(A)=0.4, P(B)=0.3, and P(A⋂▒〖B)=0.2〗.
Find the probability that a student has taken statistics or chemistry.
Find the probability that a student has taken not statistics and not chemistry.
Find the probability that a student has taken statistics but not chemistry.
Fine the probability that a student taken chemistry, given that he has taken statistics.
Answer by ikleyn(53996) About Me  (Show Source):
You can put this solution on YOUR website!
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Let A be the event that a randomly selected college student has taken a statistics course and
let B be the event that the same student has taken a chemistry course.
Suppose P(A)=0.4, P(B)=0.3, and P(A⋂B)=0.2.
(a) Find the probability that a student has taken statistics or chemistry.
(b) Find the probability that a student has taken not statistics and not chemistry.
(c) Find the probability that a student has taken statistics but not chemistry.
(d) Find the probability that a student taken chemistry, given that he has taken statistics.
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(a)  They want you find P(A U B).

     Use the standard formula  P(A U B) = P(A) + P(B) - P(A⋂B).

     Substitute the given numbers in the formula and get the answer

         P(A⋂B) = 0.4 + 0.3 - 0.2 = 0.5.



(b)  P(not statistic and not chemistry = 1 - P(A U B) = 1 - 0.5 = 0.5.



(c)  P(statistics but not chemistry) = P(A) - P(A⋂B) = 0.4 - 0.2 = 0.2.



(d)  Use the formula for conditional probability

                           P(Chem ⋂ Statistics)       P(A⋂B)      0.2
     P(Chem|Statistic) = ------------------------- = --------- = ------ = 0.5.
                              P(Statistics)             P(A)       0.4

Solved.