The secretary in exercises 2.121 and 3.16 was given n computer passwords and tries the passwords at random. exactly one of the passwords 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 what is the probability that the correct password is found on the sixth try?

There is a 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

The probability that a password is incorrect is .

There are 6 tries.

We want the first five to be wrong. So each one of the first five tries has a probability of . So, for the first five tries, the probability of getting the desired outcome is .

We want to get it right at the sixth try. The probability of sixth try being correct is .

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

There is a probability that the correct password is found on the sixth try.

step-by-step explanation:

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.