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arlik [135]
3 years ago
6

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?
Mathematics
1 answer:
Dominik [7]3 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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3 years ago
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Answer: <u>96</u> sq ft.

Step-by-step explanation:

      First, we will find the area of the rectangular sides. Since the triangle is an equilateral triangle, all the rectangles will be the same size.

             A = L * W

             A = (10 ft) * (3 ft)

             A = 30 ft²

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      Next, we will find the area of the two triangles.

             A = \frac{b*h}{2}

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1 year ago
If 1/2 hour Naomi stretches her neck; every 1/3 hour she stretches her legs; and every 1/6 hour she stretches her ams. Which par
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Legs: In 2/3 of an hour, she will stretch her legs twice (1 stretch every 1/3 of an hour for 2/3 of an hour equals 2).
Arms: In 2/3 of an hour she will stretch her arm four times (2/3 divided by 1/6 equals 4). 

Total stretches: 1 neck stretch, 2 legs stretches, and 4 arms stretches.
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3 years ago
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