tylag
contestada

A randomly generated password contains four characters. Each of the four characters is either a lowercase letter or a digit from 0–9. Each character in the password cannot be used more than once.
HELP QUICKLY PLEASE
What is the approximate probability that exactly one of the four characters will be a number?

1%
11%
28%
44%

Respuesta :

Sample space is 36C4
Now, we want to know all of the combinations that have 1 digit in it.
So, we can have one here:

1XXX
X1XX
XX1X
XXX1

But we have 10 different digits to choose from. So, we need to introduce the combination term, nCr, where n is a list of all digits and r is how many we want.

Since we only want one, we will need 10C1 for the number of digits. But we need to choose three lowercases, so it becomes 10C1 × 26C3

Since it's a probability question, we need to divide that by our sample space, 36C4, and our percentage becomes 44%

Using the permutation formula, it is found that the approximate probability that exactly one of the four characters will be a number is of 44%.

What is a probability?

  • A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, the order is important, as a different order means a different password, hence the permutation formula is used.

What is the permutation formula?

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, the total outcomes are given by 4 characters from a set of 36(26 lower-case letters and 10 digits), hence:

[tex]T = P_{36,4} = \frac{36!}{32!} = 1413720[/tex]

For the desired outcomes, we have:

  • One number from a set of 10.
  • Three letters from a set of 26.
  • 4 possible arrangements(N-L-L-L, L-N-L-L, L-L-N-L, L-L-L-N), hence:

[tex]D = 4P_{10,1}P_{26,3} = 4\frac{10!}{9!}\frac{26!}{23!} = 624000[/tex]

Hence, the probability is of:

[tex]p = \frac{D}{T} = \frac{624000}{1413720} = 0.4414[/tex]

Hence of approximately 44%.

You can learn more about the permutation formula at https://brainly.com/question/25925367

Otras preguntas