SOLUTION: Of the 58 people who answered "yes" to a question, 10 were male. Of the 95 people that answered "no" to the question, 6 were male. If one person is selected at random from the

Question 1008795: Of the 58 people who answered "yes" to a question, 10 were male.
Of the 95 people that answered "no" to the question, 6 were male.
If one person is selected at random from the group, what is the
probability that the person answered "yes" or was male?
Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

We make this chart:

       | MALE |FEMALE|TOTALS|
----------------------------|
YES    |      |      |      |
----------------------------|
NO     |      |      |      |
----------------------------|
TOTALS |      |      |      |
-----------------------------

>>Of the 58 people who answered "yes" to a question, 10 were male.

So we put 58 in the TOTALS column of the YES, and 10 in the MALE
column of the YES row:

       | MALE |FEMALE|TOTALS|
----------------------------|
YES    |  10  |      |  58  |
----------------------------|
NO     |      |      |      |
----------------------------|
TOTALS |      |      |      |
-----------------------------

Of the 95 people that answered "no" to the question, 6 were male.

So we put 95 in the TOTALS column of the NO row, and 6 in the MALE
column of the NO row:

       | MALE |FEMALE|TOTALS|
----------------------------|
YES    |  10  |      |  58  |
----------------------------|
NO     |   6  |      |  95  |
----------------------------|
TOTALS |      |      |      |
-----------------------------

Next we fill in the bottom right corner, the TOTALS row and the
TOTALS column by adding 58+95, getting 153:

       | MALE |FEMALE|TOTALS|
----------------------------|
YES    |  10  |      |  58  |
----------------------------|
NO     |   6  |      |  95  |
----------------------------|
TOTALS |      |      | 153  |
-----------------------------

Next we fill in the TOTAL MALES by adding 10+6, getting 16

       | MALE |FEMALE|TOTALS|
----------------------------|
YES    |  10  |      |  58  |
----------------------------|
NO     |   6  |      |  95  |
----------------------------|
TOTALS |  16  |      | 153  |
-----------------------------

Next we fill in the FEMALES who said YES by subtracting 58-10=48,

       | MALE |FEMALE|TOTALS|
----------------------------|
YES    |  10  |  48  |  58  |
----------------------------|
NO     |   6  |      |  95  |
----------------------------|
TOTALS |  16  |      | 153  |
-----------------------------

Next we fill in the FEMALES who said NO by subtracting 95-6=89,

       | MALE |FEMALE|TOTALS|
----------------------------|
YES    |  10  |  48  |  58  |
----------------------------|
NO     |   6  |  89  |  95  |
----------------------------|
TOTALS |  16  | 137  | 153  |
-----------------------------

Now we fill in the TOTAL FEMALES two ways, 
(1) by adding 48+89=137, and also, as a check,
by subtracting 153-16=137.

If one person is selected at random from the group, what is the
probability that the person answered "yes" or was male?

The numerator is the number who said YES or was MALE.
The ones that fit at least one of those categories are colored red:

       | MALE |FEMALE|TOTALS|
----------------------------|
YES    |  10  |  48  |  58  |
----------------------------|
NO     |   6  |  89  |  95  |
----------------------------|
TOTALS |  16  | 137  | 153  |
-----------------------------

We add the red numbers: 10+48+6 = 64.  That's how many either
said YES or were MALE.

So the probability is 64 out of the total 153 in the lower right
corner, 153, so the desired probability is 64/153.

Edwin

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