SOLUTION: A group of students were surveyed to determine their choices of surfing internet and using library to gather new information for assignment. The results showed that 85% will surf t

Question 1206437: A group of students were surveyed to determine their choices of surfing internet and using library to gather new information for assignment. The results showed that 85% will surf the internet, while only 25% will go to library. Given that among those who will surf the internet, 15% will go to library.
(i) What is the percentage of the students will use both methods to gather new information?
(ii) What percentage of the students will use at least one of the ways to get new information?
(iii) Are the events "the students who will surf the internet" and "the students who will go to library" mutually exclusive?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
A group of students were surveyed to determine their choices of surfing internet
and using library to gather new information for assignment. The results showed
that 85% will surf the internet, while only 25% will go to library.
Given that among those who will surf the internet, 15% will go to library.
(a) What is the percentage of the students will use both methods to gather new information?
(b) What percentage of the students will use at least one of the ways to get new information?
(c) Are the events "the students who will surf the internet" and "the students who will
go to library" mutually exclusive?
~~~~~~~~~~~~~~~~~

(a)  P(both library AND the Internet) = 0.85*0.15 = 0.1275,  or  12.75%.    ANSWER



(b)  P(at least one of the ways) = P(library) + P(Internet) - P(both) = 

                                 = 0.85 + 0.25 - 0.1275 = 0.9725, or 97.25%.    ANSWER


(c)  These events have the non-zero intersection, as found out in (a).
     So, they are not mutually exclusive.

Solved.

==========================

Comment from student: Hi ikelyn. Thanks for your answer.
May I know why do we multiply 0.85 with 0.15 instead of multiplying 0.85 with 0.25?

My response. The problem clearly says that the intersection "both" is 0.15 of 0.85.

Therefore I multiply 0.85*0.15 to find the measure of the intersection.

We have all the instructions and the reasons to multiply 0.85 by 0.15,
and we have NO any reason to multiply 0.85 by 0.25.

Thank you for your question.
Hope, my answer clarifies this situation.

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