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Assume that the business makes a profit with probability 0.8 in the first year. For each year thereafter, the business makes a p

Ivenika [448]

Answer:

The probability that the business makes a profit in exactly two of its first three years is 0.628.

Step-by-step explanation:

Given : Assume that the business makes a profit with probability 0.8 in the first year. For each year thereafter, the business makes a profit with probability 0.9 if it made a profit in the previous year, and with probability 0.2 if it did not make a profit in the previous year.

To find : What is the probability that the business makes a profit in exactly two of its first three years?

Solution :

Let X be the event that the business makes profit.

Y be the event that the business doesn't .

The business makes a profit with probability 0.8 in the first year.

For each year thereafter, the business makes a profit with probability 0.9.

It did not make a profit in the previous year is 0.2.

According to question,

The business makes a profit in exactly two of its first three years which is given by, XXY, XYX, YXX

So,

$P(XXY)=0.8\times 0.9\times (1-0.2)$

$P(XXY)=0.8\times 0.9\times 0.8$

$P(XXY)=0.576$

$P(XYX)=0.8\times (1-0.9)\times 0.2$

$P(XYX)=0.8\times 0.1\times 0.2$

$P(XYX)=0.016$

$P(YXX)=(1-0.8)\times 0.9\times 0.2$

$P(YXX)=0.2\times 0.9\times 0.2$

$P(YXX)=0.036$

The probability that the business makes a profit in exactly two of its first three years is given by,

P= P(XXY)+P(XYX)+P(YXX)

P= 0.576+0.016+0.036

P= 0.628

Therefore, The probability that the business makes a profit in exactly two of its first three years is 0.628.

= 0.272

7 0

3 years ago

Steven fill 3 pages in a stamp album. this is one sixth of the pages in the album. how many pages are there in steven stamp albu

Arturiano [62]

3 pages x 6 times=18 pages

7 0

4 years ago

5x = y +6<br> 5x + 2y = 3<br> I forgot how to solve it I need help

EastWind [94]

Answer:

Y=3

X=9/5

Step-by-step explanation:

(1) 5x=y+6

(2) 5x+2y =3

Replace (1) to (2) => (y+6)+2y=3 => y=3

Replace y=3 to (2) => 5x = 3+6 => 5x=9 => x=9/5

3 0

3 years ago

180 is applied to rectangle KLMN. what rectangle shows the final image ?

cricket20 [7]

Answer:

3

Step-by-step explanation:

4 0

3 years ago

Q. 3. On a recent math test, Aubrey was asked to find the LCD of and and then to write equivalent fractions using this LCD. Aubr

Darina [25.2K]

The Lowest Common Denominator of 3 and 4 is the denominator that will

simplify mathematical operations such as addition of the fractions.

The mistake is the LCD of 3 and 4 is 12 rather than 24

Reasons:

The given fractions are;

$\displaystyle \frac{1}{3} \ and \ \mathbf{\frac{2}{4}}$

The Lowest Common Denominator, is given by the Least Common Multiple of the denominators, which is 3 × 4 = 12

Therefore;

The LCD = 12

The equivalent fractions are therefore;

$\displaystyle \frac{1}{3 } = \frac{4 \times 1}{4 \times 3} = \mathbf{\frac{4}{12}}$

$\displaystyle \frac{2}{4} =\frac{3 \times 2}{3 \times 4} = \mathbf{ \frac{6}{12}}$

$\displaystyle The \ equivalent \ fractions \ are \ \frac{4}{12} \ and \ \frac{6}{12}$

Therefore, the mistake is using a LCD of 24 rather than 12, given that 12 is lower than 24 and therefore is the LCD of 3 and 4.

By having an LCD of 12, we have;

The equivalent fractions with the LCD will be; $\displaystyle \frac{4}{12} \ and \ \frac{6}{12}$

Learn more about Lowest Common Denominator, LCD here:

brainly.com/question/255303

5 0

3 years ago