A safe has a 4-digit lock code that does not …

Mathematics Questions

Step by Step Solution

Mathematics Questions

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 that the lock code consists of all even digits? To find the total number of outcomes for this event, find the permutation of ings taken 4 at a time. The total number of outcomes is The total number of favorable outcomes is a permutation of things taken 4 at a time The probability that the lock code consists of all even digits is out of 3,024.

Short Answer

The process involves calculating the permutation of 9 items taken 4 at a time, yielding a total of 3,024 outcomes. Among these, there are 24 favorable outcomes, leading to a probability of 24 out of 3,024 for selecting all even digits in the lock code.

Step-by-Step Solution

Step 1: Determine Total Outcomes

To find the total number of outcomes for selecting items from a group, calculate the permutation of 9 things taken 4 at a time. This involves finding the number of ways to arrange 4 items selected from a total of 9. The calculation results in a total of 3,024 outcomes.

Step 2: Identify Favorable Outcomes

Next, calculate the total number of favorable outcomes. This considers only the arrangements of a subset of items‚ÄöAiin this case, the permutation of 4 things taken 4 at a time. This results in exactly 24 favorable outcomes, as all 4 chosen items must be used.

Step 3: Calculate the Probability

Finally, find the probability that the lock code consists of all even digits by dividing the total number of favorable outcomes by the total number of outcomes. Thus, the probability is expressed as 24 out of 3,024, simplifying to give a clear understanding of the likelihood of this event occurring.

Related Concepts

Permutation

A mathematical operation that calculates the number of ways to arrange a subset of items from a larger set, where the order of arrangement matters.

Favorable Outcomes

The specific results of an experiment or event that align with the desired criteria or conditions, representing success in the context of probability.

Probability

A measure of the likelihood that a particular event will occur, expressed as a ratio of favorable outcomes to total outcomes.

Table Of Contents

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 that the lock code consists of all even digits? To find the total number of outcomes for this event, find the permutation of ings taken 4 at a time. The total number of outcomes is The total number of favorable outcomes is a permutation of things taken 4 at a time The probability that the lock code consists of all even digits is out of 3,024.