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In a city school of 1,200 students, 40% of the students are on the honor roll, 60% have a part-time job, and 22% are on the honor roll and have a part-time job. What is the probability (rounded to the nearest whole percent) that a randomly selected student is on the honor roll, given that the student has a part-time job?

 

A 55%

B 24%

C 13%

D 37%

hay24  Apr 12, 2018
edited by hay24  Apr 12, 2018
edited by hay24  Apr 12, 2018
 #1
avatar+7324 
+2

If you have a bag of 10 marbles, where 3 of them are blue and 7 of them are green...

 

probability that a randomly selected marble is blue  =  \(\frac{\text{num of } \underline{\text{marbles}} \text{ that are blue}}{\text{total num of }\underline{\text{marbles}}}\)

 

Likewise....

 

probability that a randomly selected student with a part time job is on the honor roll  =

 

\(\frac{\text{num of } \underline{\text{students with a part time job}} \text{ that are on the honor roll}}{\text{total num of }\underline{\text{students with a part time job}}}\)

 

num of students with a part time job that are on the honor roll  =  22% of 1200

num of students with a part time job that are on the honor roll  =  0.22(1200)

 

num of students with a part time job  =  60% of 1200

num of students with a part time job  =  0.6(1200)

 

probability that a randomly selected student with a part time job is on the honor roll  =

 

\(\frac{0.22(1200)}{0.6(1200)}\,=\\~\\ \frac{0.22}{0.6}\,=\\~\\ \frac{22}{60}\,\approx\\~\\ 37\%\)

 

I hope that made some sort of sense....

hectictar  Apr 12, 2018
edited by hectictar  Apr 12, 2018
 #2
avatar+165 
+2

omg yes thankyou so much!

hay24  Apr 12, 2018

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