SOLUTION: A recent survey found that about 18.2% of Christians were Protestants, and of those, 21.1% were left-handed. Right-handed people, however, make up 70.6% of the Catholics. Choose

Algebra ->  Probability-and-statistics -> SOLUTION: A recent survey found that about 18.2% of Christians were Protestants, and of those, 21.1% were left-handed. Right-handed people, however, make up 70.6% of the Catholics. Choose       Log On


   



Question 1182924: A recent survey found that about 18.2% of Christians were Protestants, and
of those, 21.1% were left-handed. Right-handed people, however, make up
70.6% of the Catholics. Choose one Christian at random. Find the probability
that the Christian is a left-handed Catholic.

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Make this chart:

              Catholic|Protestant|Christians 
-------------|--------|----------|----------
Right-handed |        |          |
-------------|--------|----------|----------  
Left-handed  |        |          |
-------------|--------|----------|----------
 Total %     |        |          | 100%

A recent survey found that about 18.2% of Christians were Protestants,
We fill in 18.2% for the total percent of Protestants.  Then we subtract
that from 100% and fill in 81.8% for the total percent of Catholics.

              Catholic|Protestant|Christians
-------------|--------|----------|----------
Right-handed |        |          |  
-------------|--------|----------|----------  
Left-handed  |        |          |
-------------|--------|----------|----------
 Total %     |  81.8% |  18.2%   | 100%


and of those (Protestants), 21.1% were left-handed.
We take 21.1% of 18.2% and fill in 3.8402% for the
total percent of left-handed Protestants. Then subtract
that from 18.2% and fill in 14.3598% for the total % of
Right-handed Protestants:


              Catholic|Protestant|Christians 
-------------|--------|----------|----------
Right-handed |        |14.3598%  |
-------------|--------|----------|----------  
Left-handed  |        | 3.8402%  |
-------------|--------|----------|----------
 Total %     |  81.8% |  18.2%   | 100%

Right-handed people, however, make up 70.6% of the Catholics.
 We take 70.6% of 81.8% and fill in 57.7508% for the
total percent of Right-handed Catholics. Then subtract
that from 81.8% and fill in 24.0492% for the total % of
Left-handed Catholics:

              Catholic|Protestant|Christians
-------------|--------|----------|----------
Right-handed |57.7508%|14.3598%  |
-------------|--------|----------|----------  
Left-handed  |24.0492%| 3.8402%  |
-------------|--------|----------|----------
 Total %     |  81.8% |  18.2%   | 100%

Then we finish the table by adding the percentages of right-handed
and left-handed Catholics and the percentages of right-handed
and left-handed Catholics. We fill in the total percentages of Right-handed
Christians as 72.1106% for Right-handed Christians and 27.8894% as
the total percentages of Left-handed Christians.

              Catholic|Protestant|Christians
-------------|--------|----------|----------
Right-handed |57.7508%|14.3598%  | 72.1106%
-------------|--------|----------|----------  
Left-handed  |24.0492%| 3.8402%  | 27.8894%
-------------|--------|----------|----------
 Total %     |  81.8% |  18.2%   | 100%

We now check to see if we have done our calculations correctly by adding
the percentages of right and left handed Christians to see if we get 100%.
We do!

Choose one Christian at random. Find the probability that the Christian is a
left-handed Catholic.
We see that the probability is 24.0492%.

Edwin