The accompanying data were obtained from the financial aidReceivingFinancialAidRecFinUndergraduates34,2261,873GraduatesTotal6,0994Let A be the event that a student selected at random from th(a) Find each of the following probabilities. (Round yP(A) =P(B) =P(A N B) =P(B | A) =P(B | A^) =%3D%3D

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Description: The accompanying data were obtained from the financial aidReceivingFinancialAidRecFinUndergraduates34,2261,873GraduatesTotal6,0994Let A be the event that a student selected at random from th(a) Find each of the following probabilities. (Round yP(A)

Given a data from financial aid office of a university Receiving financial aid Not receiving…

Answered: The accompanying data were obtained…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....

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The accompanying data were obtained from the financial aid
Receiving
Financial
Aid
Rec
Fin
Undergraduates
3
4,226
1,873
Graduates
Total
6,099
4
Let A be the event that a student selected at random from th
(a) Find each of the following probabilities. (Round y
P(A) =
P(B) =
P(A N B) =
P(B | A) =
P(B | A^) =
%3D
%3D

Expert Solution

Step 1

Given a data from financial aid office of a university

	Receiving financial aid	Not receiving financial aid	Total
Undergraduates	4226	3896	8122
Graduates	1873	739	2612
Total	6099	4635	10734

A is the event that a student selected at random from this university is an undergraduate student.

B is the event that a student selected at random is receiving financial aid.

Step 2

Consider the formula for probability of an event X as:

$P (X) = \frac{N u m b e r o f f a v o r a b l e o u t c o m e s}{T o t a l n u m b e r o f f a v o r a b l e o u t c o m e s}$

(a) Total number of students in university is 10734. Hence total number of favorable outcomes will be

$N (U) = 10734$

A is the event that a student selected at random from this university is an undergraduate student. Since number of undergraduate students is 8122. Hence number of favorable outcomes is

$N (A) = 8122$

Hence probability of A will be

$\begin{array}{rcl} P (A) & = & \frac{N (A)}{N (U)} \\ = & \frac{8122}{10734} \\ = & 0.75666 \\ \approx & 0.757 \end{array}$

Now B is an event that a student selected at random is receiving financial aid. Since number of students receiving financial aid is 6099. Hence number of favorable outcomes is

$N (B) = 6099$

Hence probability of B will be

$\begin{array}{rcl} P (B) & = & \frac{N (B)}{N (U)} \\ = & \frac{6099}{10734} \\ = & 0.56819 \\ \approx & 0.568 \end{array}$

Now event $A \cap B$ means student selected at random from university is an undergraduate student and receiving financial aid. Since number of undergraduate students receiving financial aid is 4226. Hence number of favorable outcomes is

$N (A \cap B) = 4226$

Hence the probability of $A \cap B$ will be

$\begin{array}{rcl} P (A \cap B) & = & \frac{N (A \cap B)}{N (U)} \\ = & \frac{4226}{10734} \\ = & 0.39370 \\ \approx & 0.394 \end{array}$

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