SOLUTION: In a group of 16 people, 8 read The Hobbit and 5 saw the movie, and 2 of the people who read the book also saw the movie. What is the probability of randomly selecting a person who

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In a group of 16 people, 8 read The Hobbit and 5 saw the movie, and 2 of the people who read the book also saw the movie. What is the probability of randomly selecting a person who      Log On


   

Question 1199830: In a group of 16 people, 8 read The Hobbit and 5 saw the movie, and 2 of the people who read the book also saw the movie. What is the probability of randomly selecting a person who has NOT read The Hobbit and who has NOT seen the movie?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Draw a rectangle to represent the universal set.
Inside the rectangle, draw partially overlapping circles which I'll label as R and S.

R = set of people who read the book
S = set of people who saw the movie



Now write "2" without quotes in the overlapped region of the circles.

These are the 2 people who read the book and saw the movie.

8 people read the book, and 2 did both, which means 8-2 = 6 read the book but didn't see the movie.
This value goes in circle R but outside circle S.

5 people saw the movie, and 2 did both, which means 5-2 = 3 saw the movie but didn't read the book.
This value goes in circle S but outside circle R.

Let's update the diagram

Side notes:
  • The values in circle R add to 6+2 = 8 who read the book.
  • The values in circle S add to 2+3 = 5 who saw the movie.
Add the values in the circles: 6+2+3 = 11
There are 11 people who read the book, saw the movie, or both.

16 total people are present. It tells us 16-11 = 5 people did not read the book nor did they see the movie.

The "5" will go outside both circles, but stay inside the universal set.

Final Venn Diagram


The goal is to select someone who hasn't seen the movie nor read the book. There are 5 such people out of 16 total.
This forms the probability 5/16.


Answer: 5/16
5/16 = 0.3125 when converting to decimal form. This value is exact without any rounding done to it.
0.3125 = 31.25%

Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.

English speaking people would prefer to say  " Neither - Nor "  instead of using doubled  " has  NOT . . . and  has  NOT . . . ".



It is not only the language preference.

In  English,  this  " Neither - Nor "  has more precise meaning than doubled  "has  NOT . . . and  has  NOT . . . "

whose meaning is  (formally)  ambiguous.


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


comment from student:   This exercise is a translation and of an exercise in Spanish.
I am not an expert translating into English.  Sorry.  But the first answer solved above is the correct.


My response:   to me,  it is  OBVIOUS  from the first glance,  that it is a translation from other language.