SOLUTION: The dress code at a North High School allows students to wear blue or white shirts. A group of students was observed and their shirt color was recorded. males

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Question 1143213: The dress code at a North High School allows students to wear blue or white
shirts.
A group of students was observed and their shirt color was recorded.

males females
blue 26 73
white 62 41

What is the probably that a student chosen is wearing a blue shirt if you
already know the student is a female P(B|F)?
Round answers to hundredths as needed.

Answer by Edwin McCravy(20060) (Show Source):
You can put this solution on YOUR website!
The dress code at a North High School allows students to wear blue or white
shirts. A group of students was observed and their shirt color was
recorded.

males females -------------------------- blue | 26 | 73 -------------------------- white| 62 | 41 -------------------------- When you have a chart like this, you should always add on a third column and a third row to the table for the totals, like below. Then you can answer any question they give you. males females totals ----------------------------------- blue | 26 | 73 | 99 | ---------------------------------- white | 62 | 41 | 103 | ---------------------------------- totals| 88 | 114 | 202 | ---------------------------------- Notice that we get the same grand total 202 whether we add the totals of the males and females 99+103 or whether we add the totals of blue shirted people and white shirted people 88+114.

What is the probably that a student chosen is wearing a blue shirt if you
already know the student is a female P(B|F)?
Round answers to hundredths as needed.

Since we already know that the student chosen is a female, we can reduce the sample space by eliminating all the males and totals on the right column, since they are not involved: females ----------------------------------- blue | | 73 | | ---------------------------------- white | | 41 | | ---------------------------------- totals| | 114 | | ---------------------------------- So the probability is 73 out of 114 or 73/114 which equals 0.6403508772 which rounds to 0.64 If you had been asked instead:

What is the probably that a student chosen is male if you already
know the student is wearing a white shirt? P(M|W)?

Since we already know that the student chosen is wearing a white shirt, we can reduce the sample space by eliminating all the people wearing blue shirts and totals on the bottom, since they are not involved: males females totals ----------------------------------- blue | | | | ----------------------------------- white | 62 | 41 | 103 | ----------------------------------- totals| | | | ----------------------------------- So the probability is 62 out of 103 or 62/103 which equals 0.6019417476 which rounds to 0.60 Yes I know you weren't asked that but you might be sometime. Edwin