Question

A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. What is the probability

Answer 1

Answer: the probability is of 0.79%

Step-by-step explanation:

There are 4 numbers, 0 not included, and there is no number repeated.

First, the total number of combinations will be:

c1 = 9*8*7*6 = 3024

this is because the first number has 9 possibilities to chose, the second will have 8 possibilities, because one number is already taken, and so on.

Now, we have 4 even numbers: 2, 4, 6, 8

the total possible combinations of those 4 numbers are calculated in the same way: the first number has 4 possibilities, the second has 3, and so on

c2 = 4*3*2*! = 24

now, the probability that the code consists only in even numbers is equal to the number of combinations of only pair numbers divided the total number of combinations:

p = c2/c1 = 24/3024 = 0.0079

for a percentage, we multiply this number by 100%

0.0079*100% = 0.79%

Answer 2

Answer:

To find the total number of outcomes for this event, find the permutation of  ⇒ 9 things taken 4 at a time.

The total number of outcomes is  ⇒ 3,024.

The total number of favorable outcomes is a permutation of  ⇒ 4 things taken 4 at a time.

The probability that the lock code consists of all even digits is  ⇒ 24 out of 3,024.