Probability of Getting a Multiple of 5 or an Even Number

When a number between 1 and 10 is chosen at random, the probability of getting a multiple of 5 or an even number is 0.7. This article will break down the calculation process to understand this concept better.

Understanding the Problem

Let's consider a set of numbers from 1 to 10. The set is as follows:

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

We want to find the probability of selecting a number that is either a multiple of 5 or an even number. Let's start by identifying the multiples of 5 and the even numbers within this range.

Multiples of 5

The multiples of 5 within the range 1 to 10 are:

[5, 10]

Even Numbers

The even numbers within the range 1 to 10 are:

[2, 4, 6, 8, 10]

Overlapping Numbers

There is one number that is both a multiple of 5 and an even number, which is 10. Therefore, the numbers that are either a multiple of 5 or an even number are:

[2, 4, 5, 6, 8, 10]

Total Outcomes and Calculation

The total number of outcomes is 10, as there are 10 numbers in the set. The number of favorable outcomes (numbers that are either a multiple of 5 or an even number) is 6. Therefore, the probability is calculated as:

[P frac{text{Number of favorable outcomes}}{text{Total number of outcomes}} frac{6}{10} 0.6]

It's important to note that there was a slight error in the initial problem statement, which stated the probability as 0.7. The correct probability is 0.6, or 60%, based on the accurate count of favorable outcomes.

Additional Insights

Further, if we consider only the even numbers that are greater than 5, the set changes. The numbers that are even and greater than 5 are:

[6, 8, 10]

There are 3 such numbers, making the probability:

[P frac{3}{10} 0.3]

This represents a 30% chance of selecting a number from the set of 10 that meets this criteria.

Conclusion

In summary, the probability of selecting a number between 1 and 10 that is either a multiple of 5 or an even number is 0.6, or 60%. This demonstrates the importance of careful counting and understanding the intersection of sets in probability calculations.