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2 years ago

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Three people get into an empty elevator at the first floor of a building that has 10 floors. Each presses the button for their d

esired floor (unless one of the others has already pressed that button). Assume that they are equally likely to want to go to floors 2 through 10 (independently of each other). What is the probability that the buttons for 3 consecutive floors are pressed?

1 answer:

Dominik [7]2 years ago

4 0

Answer:

The probability that the buttons for 3 consecutive floors are pressed is $\frac{1}{12}$ or 0.0833

Step-by-step explanation:

Consider the provided information.

They are equally likely to want to go to floors 2 through 10.

That means the number of buttons are 9.

Each presses the button for their desired floor (unless one of the others has already pressed that button).

It means that if two people wants to go at the same floors, then only one person will press the button.

Therefore, the total number of ways are: 9×8×7=504

Three consecutive floors means they have been picked:

2,3,4 or 3,4,5 or 4,5,6 or 5,6,7 or 6,7,8 or 7,8,9 or 8,9,10

We have 3 persons that means we can arrange them in 3! ways.

Therefore, the total number of favorable outcomes for this case is 7×3!=42

$Probability = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

$Probability = \frac{42}{504}=\frac{1}{12}$

Hence, the probability that the buttons for 3 consecutive floors are pressed is $\frac{1}{12}$ or 0.0833

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Ephemeral services corporation (esco) knows that nine other companies besides esco are bidding for a $900,000 government contrac

EastWind [94]

Answer:

c. $100,000

Step-by-step explanation:

Calculation of the expected net profit of Ephemeral services corporation

Since we are been told that 9 other companies besides esco are as well bidding for the $900,000 government contract, it means we have to find the expected net profit by dividing 1 by 9×$900,000 .Thus ESCO can only expect to cover its sunk cost.

Hence ,

E(X) = (1/9) × $900,000

E(X)=0.111111111×$900,000

E(X)= $100,000

Therefore the expected net profit would be $100,000

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1 year ago

−15x+4≤109 OR −6x+70>−2

Xelga [282]

$-15x+4\leq109\qquad\text{subtract 4 from both sides}\\\\-15x\leq105\qquad\text{change the signs}\\\\15x\geq-105\qquad\text{divide both sides by 15}\\\\\boxed{x\geq-7}\\or\\-6x+70>-2\qquad\text{subtract 70 from both sides}\\\\-6x>-72\qquad\text{change the signs}\\\\6x$

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2 years ago

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Which of the following statements must be true in order for the line represented by the equation y = mx + b to have a negative x

inn [45]

First option: <span>The signs of the values of m and b are the same.</span>

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2 years ago

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Is AB parallel to Bo? Explain.

Svetradugi [14.3K]

Answer:

AB parallel to CD because both lines have a slope of

of 4/3

Step-by-step explanation:

The question is not complete, there is no graph.

A graph for the question is attached below.

From the image attached below, line 1 passes through points A = (-3, -3) and point B = (0, 1) while line 2 passes through point C = (0, -5) and point D = (3, -1).

Two parallel are said to be parallel if the have the same slope. The slope of a line passing through points:

$(x_1,y_1)\ asnd\ (x_2,y_2).\ The\ slope \ is\ given\ as:\\\\Slope(m)=\frac{y_2-y_1}{x_2-x_1}$

Line 1 passes through points A = (-3, -3) and point B = (0, 1), the slope of line 1 is:

$Slope(m)=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-3)}{0-(-3)}=\frac{1+3}{0+3}=\frac{4}{3}$

Line 2 passes through point C = (0, -5) and point D = (3, -1). the slope of line 2 is:

$Slope(m)=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-(-5)}{3-0}=\frac{-1+5}{3}=\frac{4}{3}$

Therefore AB parallel to CD because both lines have a slope of

of 4/3

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2 years ago

A construction company is considering submitting bids for contracts of three different projects. The company estimates that it h

julsineya [31]

Answer:

a. $P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

b. $E(x) = 0.3$

c. $S(x)=0.5196$

d. $E=5,000$

Step-by-step explanation:

The probability that the company won x bids follows a binomial distribution because we have n identical and independent experiments with a probability p of success and (1-p) of fail.

So, the PMF of X is equal to:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}\\$

Where p is 0.1 and it is the chance of winning. Additionally, n is 3 and it is the number of bids. So the PMF of X is:

$P(x)=\frac{3!}{x!(3-x)!}*0.1^{x}*(1-0.1)^{n-x}\\$

For binomial distribution:

$E(x)=np\\S(x)=\sqrt{np(1-p)}$

Therefore, the company can expect to win 0.3 bids and it is calculated as:

$E(x) = np = 3*0.1 = 0.3$

Additionally, the standard deviation of the number of bids won is:

$S(x)=\sqrt{np(1-p)}=\sqrt{3(0.1)(1-0.1)}=0.5196$

Finally, the probability to won 1, 2 or 3 bids is equal to:

$P(1)=\frac{3!}{1!(3-1)!}*0.1^{1}*(1-0.1)^{3-1}=0.243\\P(2)=\frac{3!}{2!(3-2)!}*0.1^{2}*(1-0.1)^{3-2}=0.027\\P(3)=\frac{3!}{3!(3-3)!}*0.1^{3}*(1-0.1)^{3-3}=0.001$

So, the expected profit for the company is equal to:

$E=-10,000+50,000(0.243)+100,000(0.027)+150,000(0.001)\\E=5,000$

Because there is a probability of 0.243 to win one bid and it will produce 50,000 of income, there is a probability of 0.027 to win 2 bids and it will produce 100,000 of income and there is a probability of 0.001 to win 3 bids and it will produce 150,000 of income.

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2 years ago