SOLUTION: This one just confuses me in the questions it asks and how to write them out A fish tank contains 4 large guppies, 8 small guppies, 4 large angelfish, and 4 small angelfish. a) F

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Question 1156155: This one just confuses me in the questions it asks and how to write them out
A fish tank contains 4 large guppies, 8 small guppies, 4 large angelfish, and 4 small angelfish.
a) Find P(guppy | large). Give as a reduced fraction or exact decimal. _
b) Find P(guppy). Give as a reduced fraction or exact decimal. _
Found 2 solutions by alanc, Edwin McCravy:
Answer by alanc(27)   (Show Source): You can put this solution on YOUR website!
a.) P(guppy | large) means find the probability of getting a guppy on the condition that it is large.
so the forumula should be P( guppy | large) = P(guppy and large) /P (large)
there are 8 large fish total. and there are 4 + 8 + 4 + 4 = 20 fish total
there are 12 guppies total.
P(guppy and large) = 4 / 20
P(large fish) = 8/20
P( guppy | large ) = P (guppy and large) / P (large fish) = (4/20)/ (8/20) =
4/8 = 1/2
so P(guppy | large) = 1/2
b.) P(guppy ) = 12 guppies / 20 fish = 3/5

Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
Make a chart like this:

          |  LARGE |  SMALL  || TOTALS |
----------|--------|------------------  
GUPPIES   |    4   |    8    ||   12   |
----------|--------|---------||--------|
ANGELFISH |    4   |    4    ||    8   |
==========|========|=========||========|
TOTALS    |    8   |   12    ||   20   |

 
b) Find P(guppy).


a) Find P(guppy | large).

Since we are GIVEN that it is large, we pay no attention to anything
in the chart other than the large fish.  So we line through everything
else in the chart for a conditional probability, for it isn't considered:

          |  LARGE |  SMALL  || TOTALS |
----------|--------|------------------  
GUPPIES   |    4   |    8    ||   12   |
----------|--------|---------||--------|
ANGELFISH |    4   |    4    ||    8   |
==========|========|=========||========|
TOTALS    |    8   |   12    ||   20   |



OR, you can use the formula for conditional probability and leave the
chart as is.  But you will have fractions over fractions to simplify.

          |  LARGE |  SMALL  || TOTALS |
----------|--------|------------------  
GUPPIES   |    4   |    8    ||   12   |
----------|--------|---------||--------|
ANGELFISH |    4   |    4    ||    8   |
==========|========|=========||========|
TOTALS    |    8   |   12    ||   20   |



Edwin
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