1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alexeev081 [22]
2 years ago
13

Of the entering class at a​ college, ​% attended public high​ school, ​% attended private high​ school, and ​% were home schoole

d. Of those who attended public high​ school, ​% made the​ Dean's list, ​% of those who attended private high school made the​ Dean's list, and ​% of those who were home schooled made the​ Dean's list. A student is randomly chosen. ​a) Find the probability that the student made the​ Dean's list. ​b) Find the probability that the student ​, given that the student made the​ Dean's list. ​c) Find the probability that the student ​, given that the student did not make the​ Dean's list.
Mathematics
1 answer:
Veronika [31]2 years ago
3 0

Answer:

(a) The probability that the student made the​ Dean's list is 0.1655.

(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

Step-by-step explanation:

The complete question is:

Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.

a) Find the probability that the student made the Dean's list.

b) Find the probability that the student came from a private high school, given that the student made the Dean's list.

c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.

Solution:

Denote the events as follows:

<em>A</em> = a student attended public high school

<em>B</em> = a student attended private high school

<em>C</em> = a student was home schooled

<em>D</em> = a student made the Dean's list

The provided information is as follows:

P (A) = 0.71

P (B) = 0.21

P (C) = 0.08

P (D|A) = 0.16

P (D|B) = 0.19

P (D|C) = 0.15

(a)

The law of total probability states that:

P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})

Compute the probability that the student made the​ Dean's list as follows:

P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)

         =(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655

Thus, the probability that the student made the​ Dean's list is 0.1655.

(b)

Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:

P(B|D)=\frac{P(D|B)P(B)}{P(D)}

             =\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411

Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c)

Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:

P(C^{c}|D^{c})=1-P(C|D^{c})

               =1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185

Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

You might be interested in
When using the substitution method for solving a system of linear equations in two variables, what should be the first step?
Yuri [45]
The first step would be to isolate a variable (solve for a variable)....so u will have something to sub into the other equation
8 0
3 years ago
How do you find the slope of a line on a graph
MariettaO [177]
Rise over run
find the difference between two points
5 0
3 years ago
Please help asappppp
swat32

Answer:

9........I will post process in comments because you are needing this right now

4 0
3 years ago
HELP PLEASE I have no clue what this is
devlian [24]

Answer:

972

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What number represents 125638 rounded to the nearest hundred
Evgen [1.6K]
The number is 127000...
6 0
3 years ago
Read 2 more answers
Other questions:
  • 6/10 = 1/2 true or false
    7·1 answer
  • 68/80 as a fraction,percent,and decimal
    12·1 answer
  • What is the axis of symmetry for f(x) = 2x2 − 4x + 5?
    12·2 answers
  • The objects have all the following properties in common except​
    9·1 answer
  • The normal body temperature of a camel is 37°C. This temperature varies by up to 3°C throughout the day. Write and solve an abso
    10·1 answer
  • Need some help with a few consecutive integer word problems, tysm if you do :)
    7·1 answer
  • Find the solution to the system of equations below:<br><br> y = 4x + 20<br><br> y = 8x - 4
    12·1 answer
  • PLEASE HELP -7y + 11 = 75 + y
    13·1 answer
  • What is the y-value of the vertex of 4x^+ 8x - 8?
    6·1 answer
  • Suppose 4y – 1 = 15 and y = 5x – 3.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!