(1 point) At a certain university in Western Canada, 38% of all 1st-year student
ID: 3040588 • Letter: #
Question
(1 point) At a certain university in Western Canada, 38% of all 1st-year students are registered in an introductory Calculus course, 23% are registered in an introductory Economics course, and 55% are registered in an introductory Calculus or an introductory Economics course. You randomly pick a 1st-year student from this particular university. Find the probability that the student chosen Part (a) is registered in both an introductory Calculus course and an introductory Economics course. (Use two decimals in your answer) Part (b) is registered in an introductory Calculus course and not registered in an introductory Economics course. Part (c) is not registered in introductory Calculus or not registered in introductory Economics Part (d) is not registered in either course Part (e) If a student is registered in introductory Calculus, what is the probability they are also registered in introductory Economics? four decimals) Part () ilf a student is not registered in introductory Economics, what is the probability they are also not registered in introductory Calculus? (Use two decimals) iii(use two decimals) (use two decimals) (use i(use four decimals) Part (g) Are the events "registered in introductory Calculus" and " registered in introductory Economics" independent? Select the most appropriate reason below. A. They are independent events, because P(Calculus l Economics) = P(Calculus)P(Economics). B. They are not mutually exclusive events, therefore, they must be independent events. C. They are not independent events, because P(CalculusEcnomics) P(Calculus)P(Economics). D. They are independent events, because P(Calculus n Economics) 0. E. They are not independent events, because P(Calculus n Economics) 0Explanation / Answer
Answer to the qustion is as follows:
p(calculus) = .38
p(intro. eco) = .23
p(calculus or into. eco) = .55
a. p(both) = ?
p(calculus or into eco) = p(calculus) + p(intro. eco.) - p(either)
p(both) = .38.23-.55 = .06
b. p(calculus and not eco) = p(calculus) - p(both) = .38-06 = .32
c. p(not calculus, and not eco) = 1-p(either) =1-.55 = .45 [this part is same as the d. part, as the wordings are different, but the question asked is the same]
d. p(not either) = 1-.55 = .45
e. P( intro. eco|calculus) = .06 /.38 = .1579
f. P( not calculus|not eco) = (1-.23-06)/(1-.23) = .92
g. P(calculus)*P(eco) = .874 != P(calculus and eco) = .06
So, they are not independent
c. is correct
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