Question

In a city school of 900 students, 38% of the students are on the honor roll, 54% have a part-time job, and 21% 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?

Option 1: P(ANB)
Option 2: Hint P(AB) =
Option 3: P(B)
Option 4: P(A|B)

Answer 1

The probability that a randomly selected student is on the honor roll, given that the student has a part-time job, is calculated using the formula for conditional probability and is found to be 39%.

Step-by-step explanation:

The question asks for the probability that a randomly selected student is on the honor roll, given that the student has a part-time job. In probability theory, this is known as the conditional probability, which is represented by P(A|B), where A is the event of being on the honor roll and B is the event of having a part-time job. To calculate this, we will use the formula for conditional probability, which is:

P(A|B) = P(A ∩ B) / P(B)

According to the information provided:

• 38% of the students are on the honor roll (P(A))
• 54% have a part-time job (P(B))
• 21% are on the honor roll and have a part-time job (P(A ∩ B))

To find the conditional probability, we divide the percentage of students who are both on the honor roll and have a part-time job by the percentage of students who have a part-time job:

P(A|B) = P(A ∩ B) / P(B) = 21% / 54%

Using a calculator, this gives us:

P(A|B) = 0.3889, which rounds to 39% when expressed as a whole percentage.

Therefore, the probability that a randomly selected student is on the honor roll, given that the student has a part-time job, is 39%.