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

#1**+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