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Anna [14]
3 years ago
14

The secretary in Exercises 2.121 and 3.16 was given n computer passwords and tries the passwords at random. Exactly one of the p

asswords permits access to a computer file. Suppose now that the secretary selects a password, tries it, and—if it does not work—puts it back in with the other passwords before randomly selecting the next password to try (not a very clever secretary!). What is the probability that the correct password is found on the sixth try?
Mathematics
1 answer:
Vlada [557]3 years ago
5 0

Answer:

There is a \frac{(n-1)^{5}}{n^{6}} probability that the correct password is found on the sixth try.

Step-by-step explanation:

We have n passwords, only 1 is correct.

So,

Since a password is put back with other, at each try, we have that:

The probability that a password is correct is \frac{1}{n}

The probability that a password is incorrect is \frac{n-1}{n}.

There are 6 tries.

We want the first five to be wrong. So each one of the first five tries has a probability of \frac{n-1}{n}. So, for the first five tries, the probability of getting the desired outcome is \frac{(n-1)^{5}}{n^{5}}.

We want to get it right at the sixth try. The probability of sixth try being correct is \frac{1}{n}.

So, the probability that the first five tries are wrong AND the sixth is correct is:

P = \frac{(n-1)^{5}}{n^{5}}\frac{1}{n} = \frac{(n-1)^{5}}{n^{6}}

There is a \frac{(n-1)^{5}}{n^{6}} probability that the correct password is found on the sixth try.

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Using linear function concepts, it is found that:

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  • b) f(90) = 46.6, which is the cost of 340 kWh of consumption in a month.

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

A <em>linear function </em>has the format given by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0.

The equation for the cost of h kilowatt hours (kWh) of electricity used in excess of 250 kWh is of:

C = f(h) = 37.6 + 0.1h

Item a:

  • The slope is of m = 0.1, which means that it costs $0.1 for each kilowatt hour of electricity used in excess of 250 kWh.

Item b:

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A similar problem is given at brainly.com/question/24808124

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