SOLUTION: A survey showed that 23% of college students read newspapers on a regular basis and that 83% of college students regularly watch the news on TV. The survey also showed that 21% of

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Question 314338: A survey showed that 23% of college students read newspapers on a regular basis and that 83% of college students regularly watch the news on TV. The survey also showed that 21% of college students both follow TV news regularly and read newspapers regularly.
(a) What is the probability that a student watches TV news regularly, given that he or she regularly reads newspapers? Round your answer to 2 decimal places.
(b) What is the probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly? Round your answer to 2 decimal places.

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A survey showed that 23% of college students read newspapers on a regular basis and that 83% of college students regularly watch the news on TV. The survey also showed that 21% of college students both follow TV news regularly and read newspapers regularly.
---
Sketch a 2x2 contingency table. Post the given numbers. Drive the rest
of the fills.
---------------------------------
(a) What is the probability that a student watches TV news regularly, given that he or she regularly reads newspapers? Round your answer to 2 decimal places.
Ans: 21/23
--------------------------
(b) What is the probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly? Round your answer to 2 decimal places.
Ans: 21/83
===========================================
Cheers,
Stan H.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Make this chart: 

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |         |              |           |
------------------------------------------------
Don't read |         |              |           |
newspapers |         |              |           |
------------------------------------------------
 Totals    |         |              |           |
================================================

Fill in 100% in the lower right corner, since all the
totals must be 100%:

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |         |              |           |
------------------------------------------------
Don't read |         |              |           |
newspapers |         |              |           |
------------------------------------------------
 Totals    |         |              |   100%    |
================================================

>>...A survey showed that 23% of college students read newspapers on a regular basis...<<

So we fill in 23% under the total of the "read newspapers" row.

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |         |              |    23%    |
------------------------------------------------
Don't read |         |              |           |
newspapers |         |              |           |
------------------------------------------------
 Totals    |         |              |   100%    |
================================================

>>...83% of college students regularly watch the news on TV...<<

So fill in 83% under the total of the "Watch TV" column:

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |         |              |    23%    |
------------------------------------------------
Don't read |         |              |           |
newspapers |         |              |           |
------------------------------------------------
 Totals    |   83%   |              |   100%    |
================================================

>>...21% of college students both follow TV news regularly and read newspapers regularly...<<

So fill in 21% in the space that is both in the "Watch TV" column and
the Read newspapers row, which is the upper left space:

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |   21%   |              |    23%    |
------------------------------------------------
Don't read |         |              |           |
newspapers |         |              |           |
------------------------------------------------
 Totals    |   83%   |              |   100%    |
================================================

Now we can fill in the rest of the spaces by subtracting.

The number that Read newspapers but don't Watch TV is 2%,
since 23%-21% = 2%, so we fill in 2% in the upper middle
space:

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |   21%   |      2%      |    23%    |
------------------------------------------------
Don't read |         |              |           |
newspapers |         |              |           |
------------------------------------------------
 Totals    |   83%   |              |   100%    |
================================================

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |   21%   |      2%      |    23%    |
------------------------------------------------
Don't read |         |              |           |
newspapers |         |              |           |
------------------------------------------------
 Totals    |   83%   |              |   100%    |
================================================

Since the total who Watch TV is 83%, and 21% both Watch TV and
Read newspapers, we subtract 83%-21% = 62% and put that in the
space for those who Watch TV and Don't read newspapers:

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |   21%   |      2%      |    23%    |
------------------------------------------------
Don't read |         |              |           |
newspapers |   62%   |              |           |
------------------------------------------------
 Totals    |   83%   |              |   100%    |
================================================
 
Sinc 83% total Watch TV, then 100%-83% = 17% total Don't
wath TV.  So we fill 17% in the total that don't watch TV.

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |   21%   |      2%      |    23%    |
------------------------------------------------
Don't read |         |              |           |
newspapers |   62%   |              |           |
------------------------------------------------
 Totals    |   83%   |     17%      |   100%    |
================================================

Sinc 17% total Don't watch TV, then 17%-2% = 15% Don't
watch TV and also Don't read newspapers.  So we fill 15%
in that space:

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |   21%   |      2%      |    23%    |
------------------------------------------------
Don't read |         |              |           |
newspapers |   62%   |     15%      |           |
------------------------------------------------
 Totals    |   83%   |     17%      |   100%    |
================================================

Now finally we have just one more space to fill.
And we can fill it either of two ways.

1.  The total number who Don't read newspapers is
the sum 62% + 15% = 77%

OR

2.  Since 100% either read or don't read newspapers,
The total number who Don't read newspapers is
100%-23% = 77%

Since both methods give that same last result 77%, we
know we have filled the chart correctly.

=================================================
           |  Watch  |  Don't watch |           |
           |    TV   |      TV      |  Totals   |
=================================================
  Read     |         |              |           |
newspapers |   21%   |      2%      |    23%    |
------------------------------------------------
Don't read |         |              |           |
newspapers |   62%   |     15%      |    77%    |
------------------------------------------------
 Totals    |   83%   |     17%      |   100%    |
================================================

(a) What is the probability that a student watches TV news regularly, given that he or she regularly reads newspapers? Round your answer to 2 decimal places.

(b) What is the probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly? Round your answer to 2 decimal places. 


Edwin