Question 473929: Help!!!
A class has 17 boys and 10 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).
(to three decimal places.)
P(K | F)=
P(F | K)=
Found 2 solutions by jim_thompson5910, robertb:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! P(K | F) literally means (in English): "the probability of selecting Kate given a girl/female was selected". I underlined "given" for emphasis to show that we know 100% that a girl was selected.
So if we know that a girl was selected, then what is the probability that Kate is chosen.
Take note that there are 10 girls, and only one Kate (assuming we're talking about a specific and unique "Kate"). So the probability is 
This then means that
P(K | F) =
In decimal form,  , so
P(K | F) = 0.1
Is another way to say it. Note: 0.1 is 10%
Further notes....
If the notation P(K | F) confuses you, then think of P(K | F) as P(K) given that F has occurred (or is true).
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P(F | K) is very similar, but asks the reverse: "What is the probability of selecting a female GIVEN that Kate has been chosen?"
Well, we know that Kate is a girl (since this is a natural assumption to make and because it's stated in the question). So because Kate was chosen and that she is a girl, we can say that the probability is 1 (basically 1 refers to 100%). In other words, if we know that Kate was selected, then the person MUST be a female.
So P(F | K) = 1
Answer by robertb(5830)  (Show Source):
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