Question

In: Statistics and Probability

It is estimated that 30% of university students are taking five or more classes this semester...

It is estimated that 30% of university students are taking five or more classes this semester (let us call them full-load students). Among the full-load students, 20% are working part-time. On the other hand, among the non-full-load students, 60% are working part-time.

a) When a university student is randomly selected, what is the probability that one is a full-load student and working part-time? [2]

Define event A as: university students taking five or more classes (or being full-load students).

Define event B as: university students working part-time.

b) When a university student is randomly selected, what is the probability that one is working part-time but not taking full-load? [2]

Expert Solution

It is estimated that 30% of the students are taking five or more classes this semester. They are full load students.

Among the full load students, 20% are working part time.

On the other hand, among the non full load students, 60% are working part time.

Now, let us define

A=University student being full load student.

B=University student working part time.

The information given is

Question (a)

We have to find the probability that a randomly selected student is a full load student and works part time.

So, basically we have to find

By the definition of conditional probability,

this is equal to

So, the answer is 0.06.

Question (b)

We have to find the probability that a randomly selected student is working part time but not taking full load.

So, basically we have to find

By the definition of conditional probability, this becomes

The answer is 0.42.

orchestra answered 1 year ago

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