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Keith_Richards [23]
3 years ago
11

A boiler has five identical relief valves. The probability that any particular valve will open on demand is 0.93. Assume indepen

dent operation of the valves. Calculate P(at least one valve opens). (Round your answer to eight decimal places.)
Mathematics
2 answers:
matrenka [14]3 years ago
7 0

Answer:

0.930000

Step-by-step explanation:

noname [10]3 years ago
5 0

Answer:

There is a 99.99998% probability that at least one valve opens.

Step-by-step explanation:

For each valve there are only two possible outcomes. Either it opens on demand, or it does not. This means that we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

n = 5, p = 0.93

Calculate P(at least one valve opens).

This is P(X \geq 1)

Either no valves open, or at least one does. The sum of the probabilities of these events is decimal 1. So:

P(X = 0) + P(X \geq 1) = 1

P(X \geq 1) = 1 - P(X = 0)

So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{5,0}.(0.93)^{0}.(0.07)^{5} = 0.0000016807

Finally

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0000016807 = 0.9999983193

There is a 99.99998% probability that at least one valve opens.

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A small regional carrier accepted 23 reservations for a particular flight with 20 seats. 14 reservations went to regular custome
MrRissso [65]

Answer:

- The probability that overbooking occurs means that all 8 non-regular customers arrived for the flight. Each of them has a 56% probability of arriving and they arrive independently so we get that  

P(8 arrive) = (0.56)^8 = 0.00967

- Let's do part c before part b. For this, we want an exact booking, which means that exactly 7 of the 8 non-regular customers arrive for the flight. Suppose we align these 8 people in a row. Take the scenario that the 1st person didn't arrive and the remaining 7 did. That odds of that happening would be (1-.56)*(.56)^7.

Now take the scenario that the second person didn't arrive and the remaining 7 did. The odds would be  

(0.56)(1-0.56)(0.56)^6 = (1-.56)*(.56)^7. You can run through every scenario that way and see that each time the odds are the same. There are a total of 8 different scenarios since we can choose 1 person (the non-arriver) from 8 people in eight different ways (combination).  

So the overall probability of an exact booking would be [(1-.56)*(.56)^7] * 8 = 0.06079

- The probability that the flight has one or more empty seats is the same as the probability that the flight is NOT exactly booked NOR is it overbooked. Formally,  

P(at least 1 empty seat) = 1 - P(-1 or 0 empty seats)  

= 1 - P(overbooked) - P(exactly booked)

= 1 - 0.00967 - 0.06079  

= 0.9295.

Note that, the chance of being both overbooked and exactly booked is zero, so we don't have to worry about that.

Hope that helps!

Have a great day :P

7 0
3 years ago
What is the answer in simplest term?
Burka [1]

Answer:

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--------------

2x

Step-by-step explanation:

To rationalize the denominator, we need to get rid of the square root.  We need to multiply by sqrt(12x)/sqrt(12x)

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----------  * -----------

sqrt(12x)      sqrt(12x)

9sqrt(12x)

-----------------

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We can cancel  3 in the top and bottom

3sqrt(12x)

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4x

We also notice that 12 is made up of 4 and 3

3sqrt(4) sqrt(3x)

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4x

3sqrt(4) sqrt(3x)

----------------------

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We can cancel a 2 in the top and bottom

3*sqrt(3x)

--------------

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8 0
3 years ago
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Answer:  

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Step-by-step explanation:

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3 0
2 years ago
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Maru [420]

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Korolek [52]

Answer:

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8/3+6/7=56/21+18/21=74/21 or 3 11/21

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