Question

In: Statistics and Probability

An observational study of a group of students was conducted, and students were classified in two...

An observational study of a group of students was conducted, and students were classified in two ways. First, they were each classified as to whether or not they were FullTime or PartTime. Second, they were each classified as to which of two colleges they were in, COS (college of sciences) or CBA (college of business administration). From that data, the following partial joint probability table was constructed.

FullTime PartTime
COS 7/23 3/23 ?
CBA 8/23 ? 13/23
15/23 8/23

1

Please answer the following questions about the probability of drawing students at random from this group according to the table above.  Please keep your answers as fractions (e.g., "3/7").

  • What is the marginal probability that a random student will be from COS (college of science)?  
  • What is the joint probability that a random student will be both part-time and from CBA (college of business administration)?
  • If I already know the student is from CBA, what is the probability they are a full time?

Solutions

Expert Solution

We are given the joint probability distribution of a group of students who were classified based on whether or not they were FullTime or PartTime and to which of two colleges they were in, COS or CBA.

FullTime PartTime Total
COS 7/23 3/23 ?
CBA 8/23 ? 13/23
Total 15/23 8/23 1

Students are drawn at random from this group according to the table above.

The joint probability of a FullTime COS student = 7/23

The joint probability of a PartTime COS student = 3/23

Therefore, the marginal probability of a COS student = 7/23 + 3/23 = 10/23

Answer: The marginal probability that the student will be from COS is 10/23.

The joint probability of a FullTime CBA student = 8/23

The marginal probability of a CBA student = 13/23

Therefore, the joint probability of a PartTime CBA student = 13/23 - 8/23 = 5/23

Answer: The joint probability that a random student will be both part-time and from CBA is 5/23.

If it is already know the student is from CBA, the probability they are a full time is

= P(the students are full time | the student is from CBA)

= P(the students are full time AND the student is from CBA)/P(the student is from CBA)

= (Joint probability of full time and CBA students)/(marginal probability of CBA students)

= (8/23)/(13/23)

= 8/13

Answer: If it is already know the student is from CBA, the probability they are a full time is 8/13.

orchestra answered 2 years ago
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