What is the volume of 2 liters of water?

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

Veronika [31]

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:

A = a student attended public high school

B = a student attended private high school

C = a student was home schooled

D = 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.

3 0

2 years ago

A mechanic has a radiator hose that measures 32 feet long. It needs to be cut into pieces equaling 5 feet 3 inches. How many who

kirza4 [7]

Answer:

6 pieces

Step-by-step explanation:

6x5=30

6x3=18

18-12=6

the total would be 31ft and 6 inches

6 0

3 years ago

Read 2 more answers

Translate the following phrase into an expression:The difference between 20 and twice of a number twice of a number

Vitek1552 [10]

Answer: probably D

In math difference means subtraction

Step-by-step explanation:

7 0

3 years ago

Three boxes of cereal weigh 379.4 grams,424.25 grams,and 379.37 grams. What is the difference between the lightest and the heavi

TiliK225 [7]

Answer:

44.88

Step-by-step explanation:

Heaviest box = 424.25

Lightest box = 379.37

424.25 - 379.37 = 44.88

Hope this helps!

8 0

3 years ago

For what value of x is sq 896z^15/225z^6 = xz^4/15

Ratling [72]

Answer:

Value of x is, 8

Step-by-step explanation:

Given: $\sqrt{\frac{896z^{15}}{225z^6}} =\frac{xz^4}{15} \sqrt{14z}$ ,.....[1]

To find the value of x:

Using exponent rules:

$(a^n)^m = a^{nm}$

$a^n \cdot a^m = a^{n+m}$

Taking square both sides in [1] we have;

$\frac{896z^{15}}{225z^6} = (\frac{xz^4}{15})^2 \cdot (14z)$

Simplify:

$\frac{896z^{15}}{225z^6} =\frac{x^2z^8}{225} \cdot (14z)$

or

$\frac{896z^{15}}{225z^6} =\frac{14x^2z^9}{225}$

Multiply both sides by $\frac{225}{14z^9}$ we get;

$x^2 = \frac{896 z^{15}}{225z^6} \times \frac{225}{14 z^9} = \frac{896 z^{15}}{14 z^{9+6}}$

Simplify:

$x^2 = \frac{896 z^{15}}{14 z^{15}} = 64$

or

$x = \sqrt{64}$

Simplify:

x = 8

Therefore, the value of x is, 8

5 0

3 years ago