SOLUTION: A class has 15 boys and 14 girls. One student is selected. F is the event of selecting a girl, and K is the event of selecting Kate, one of the girls in the class. Determine P(K

Algebra ->  Probability-and-statistics -> SOLUTION: A class has 15 boys and 14 girls. One student is selected. F is the event of selecting a girl, and K is the event of selecting Kate, one of the girls in the class. Determine P(K       Log On


   

Question 1082877: A class has 15 boys and 14 girls. One student is selected. F is the event of selecting a girl, and K is the event of selecting Kate, one of the girls in the class. Determine
P(K | F)
and
P(F | K).
(Round your answers to three decimal places.)
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are 14 girls
There are 15 boys
Making 15+14 = 29 students total

Let's define two events
K = event of picking Kate
F = event of picking a girl

The probability of event F is
P(F) = 14/29
since there are 14 girls out of 29 students total

The probability of event K is
P(K) = 1/29
since there's only one way to pick Kate out of 29 students total

Because Kate is a girl, this means that the event "K and F" is really just K.
Selecting Kate is the same as selecting a girl, but not the other way around.
So that's why P(K and F) = 1/29 as well.

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Round to 3 decimal places

This implies that if we're guaranteed information that we picked a female, then the chances of picking Kate are roughly 0.071 (converts to 7.1%). Since we know the selected person is female, we can ignore the males completely.

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This says "if you know you selected Kate, then the probability of picking a girl is 100%". This is due to the nature of how the sets K and F are related. K is a subset of F.

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In summary the answers are


The first result is approximate to 3 decimal places. The second result is exactly 1 indicating "100% chance of happening" or "guaranteed to happen".

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

There are 2 ways to do a conditional probability problem:
1. Reducing the sample space to just what was given.
2. Formula

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P(K|F) = P(Kate was picked|A girl was picked) = 
P(Kate was picked GIVEN THAT a girl was picked)

First way:  Reduce the sample space to just what is given, that is,
eliminate everything that is not given:

So we eliminate the 15 boys, and the sample space is the 14 girls,
Kate is 1 out of the 14 girls, so 

P(K|F) = 1/14

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P(F|K) = P(A girl was picked|Kate was picked) = 
P(A girl was picked GIVEN THAT Kate was picked)

Reduce the sample space to just what is given, that is,
eliminate everything that is not given:

So we eliminate everybody but Kate so the sample space just has one
simple event, picking Kate.  So picking 1 girl out of 1 girl is a
probability of 1/1 or 1.  

P(F|K) = 1
 
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Second way:

Use the formula:











Edwin