Question

A computer is used to generate passwords. Passwords are made up of numbers from 1–8 and lowercase letters. The computer generates passwords one character at a time. What is the probability the first character is an even number? Enter your answer, as a decimal rounded to the nearest hundredth, in the box.

Answer 1

Answer: The answer is 0.1176470588235294, or rounded to the nearest hundredth 0.11, or 11%. There are 26 letters in the alphabet, so 76% that the first character is a lowercase letter. There are 8 possibilities of a number, being 1-8. 2,4,6,and 8 are favored here as the even numbers. This means that there are 4 out of 34 possibilities of the first character being an even number. 4/34 = 0.1176470588235294 or 11%. (This answer is almost a year late so you probably won't even see this)

Edit: Actually, I forgot to round so it would be 12% or 0.12.

Answer 2

So, the first number can be any of the 10 digits (0-9). From these 10 digits, 0,2,4,6, and 8 are even numbers. The total number of even numbers is 5. Therefore, 5 numbers are not even numbers.

So, the probability that a first character is an even number is equal to the number of even divided by the total number of possible outcomes. That is,

`P\left(even\:number\right)=(5)/(5+5)=(5)/(10)\:or\:0.50`

The probability is 0.50.