SOLUTION: Here is the titanic data we are working with... died survived total female 126 344 470 male 1364 366 1730 total

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Question 103841: Here is the titanic data we are working with...
died survived total
female 126 344 470
male 1364 366 1730
total 1490 710 2200
We are asked to show why the general addition rule is true and the hint was to use Venn Diagrams.
I have done P(A or B) = p(A) + p(B) - P (A and B)
.21+.73-.32=.62 but I don't understand "how to show that the General Addition Rule is True"?
Thanks for explaning this to me.
Jessica

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What are you taking as "A" and what are you taking as "B"
--------------
The general addition rule is as you have stated it.
So you would have to choose A and B that have an
intersection, like A=survived and B=male
-------------
That way you could demonstrate the general addition rule.
================
Hope that helps
================
Cheers,
Stan H.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Solution by Edwin:

Here is the titanic data we are working with... 

         died | survived | totals
female|   126 |    344   |  470
 male |  1364 |    366   | 1730
totals|  1490 |    710   | 2200 

We are asked to show why the general addition rule 
is true and the hint was to use Venn Diagrams.

Draw a rectangle on the left for all the Males
and label it M:

 

To the right of that, draw a rectangle for all the
Females and label it F:

 

Now draw a circle in the middle for the survivors
and label it S

 

The left half of the circle contains the male
survivors, so put 366 in the left half of the
circle:



The males who died are in the left rectangle
but outside the circle. So put 1364 there:



The right half of the circle contains the female
survivors, so put 344 in the right half of the
circle:



The females who died are in the right rectangle
but outside the circle. So put 126 there:



Now to get P(M or S), we just look at this
part of the Venn diagram:



So the number in this part is 1364+366+344 = 2074
and since there were 2200 people on board, the
probablity that a person on board was either male
or survived is given by

P(M or S) = 2074%2F2200 = 1037%2F1100 

Now let's use the formula and see if we get the same answer:

P(M or S) = P(M) + P(S) - P(M and S)

P(M or S) = 1730%2F2200 + 710%2F2200 - 366%2F2200

P(M or S} = %281730%2B710-366%29%2F2200 = 2074%2F2200 = 1037%2F1100

So we see that the general sum formula does agree 
with the Venn diagram answer.

We can also do the same thing with P(F or S)

Now to get P(F or S), we just look at this
part of the Venn diagram:



So the number in this part is 366+344+126 = 836
and since there were 2200 people on board, the
probablity that a person on board was either female
or survived is given by

P(F or S) = 836%2F2200 = 19%2F50 

Now let's use the formula and see if we get the same answer:

P(F or S) = P(F) + P(S) - P(F and S)

P(F or S) = 470%2F2200 + 710%2F2200 - 344%2F2200

P(F or S} = %28470%2B710-344%29%2F2200 = 836%2F2200 = 19%2F50

So we see again that the general sum formula 
does agree with the Venn diagram answer.

Edwin