Question

A professor has noticed that, even though attendance is not a component of the final grade for the class, students that attend regularly generally get better grades. In fact, 48% of those who come to class on a regular basis receive A's. Only 6% who do not attend regularly get A's. Overall, 60% of students attend regularly. Based on this class profile, suppose we are randomly selecting a single student from this class, and answer the questions below.

Hint #1: pretend that there are 1000 students in the class and use the values given in the problem to construct the appropriate contingency table. Round cell frequencies to the nearest integer

Hint #2: No joke, you really need to use hint #1.

Hint #3: The first step to using hint #1 is to calculate the totals for those who attend regularly and do not attend regularly.

A) P(receives A's | attends regularly) =

B) P(receives A's | does not attend regularly) =

C) P(receives A's) =

D) P(attends regularly | receives A's) =

E) P(does not attend regularly | does not receive A's) =

Answer 1

Let P =Probability

Attend regularly =R

Do not attend regularly =R^c

Getting A grade =A

Not getting A grade =A^c

Given:

N =Total students =1000

60% attend regularly. So, total students who attend regularly =1000*60% =600. Thus, P(R) =600/1000 =0.6

Total students who do not attend regularly =1000-600 =400. Thus, P(R^c) =400/1000 =0.4

48% of those who come to class on a regular basis receive A's:

So, P(A/R) =0.48 P(A^c/R) =1-0.48 =0.52

Only 6% who do not attend regularly get A's:

So, P(A/R^c) =0.06 P(A^c/R^c​​​​​​) =1-0.06 =0.94

	A	not A (Ac​​​​​​)	Total
Attend regularly(R)	600*48% =288	600*52% =312	600
Do not attend regularly(Rc)	400*6% =24	400*94% =376	400
Total	312	688	1000

A) P(receives A's | attends regularly) =P(A/R) =0.48

B) P(receives A's | does not attend regularly) =P(A/R^c) =0.06

C) P(receives A's) =P(A) =312/1000 =0.312

D)

P(attends regularly | receives A's) =P(R/A) =P(A/R)*P(R)/P(A) =0.48*(600/1000)/(312/1000) =0.48*0.6/0.312 =0.9231

E)

P(does not attend regularly | does not receive A's) =P(R^c/A^c​​​​​​) =P(A^c/R^c)*P(R^c)/P(A^c) =0.94*(400/1000)/(688/1000) =0.94*0.4/0.688 =0.5465​​​​​​