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# In a city school of 1,200 students, 30% of the students are on the honor roll

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In a city school of 1,200 students, 30% of the students are on the honor roll, 62% have a part-time job, and 24% 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?

15%

39%

19%

48%

Apr 28, 2018

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Since 24% of 1200 students have a part-time job and on the honor roll,

there are $$0.24 \cdot 1200= 288$$ students that have a part-time job and on the honor roll.

there are $$0.62\cdot1200=744$$ students that have a part-time job, including the ones on the honor roll.

Since the problem states that they selected a student with a part time job, it must be one of the 744 students.

Out of the 744, we need the student to be one of the 288 people, so the probabilty of this happening is:

$$288\div744\approx0.3871$$

Rounding this to the nearest percent, we have 39%.