The Probability of Picking a Multiple of 2 Greater than 60 Between 50 and 81

Ever wondered about the odds when you're picking a number between the range of 50 and 81, specifically if you'll land on a multiple of 2 greater than 60? This article delves into the specifics of such probability calculations, providing clear explanations and practical examples. Let's explore this fascinating field and understand the underlying logic step-by-step.

Understanding the Basics: Multiples of 2

Firstly, it's essential to understand that every even number is a multiple of 2. This fundamental principle simplifies our task significantly as we only need to consider the even numbers within the given range. The range from 50 to 81 includes all the even numbers greater than 60.

Counting the Successful Events

To find the probability, we start by identifying the successful events, i.e., the multiples of 2 greater than 60 within the range. These numbers are:

62 64 66 68 70 72 74 76 78 80

Counting these, we find there are 10 successful events.

Determining the Total Number of Events

The next step is to identify the total number of possible events within the range. If we're inclusive of both 50 and 81, the total numbers between 50 and 81 are from 50 to 81 inclusive. To find this, we use the formula for the number of integers in a range:

Total number of integers (Upper limit - Lower limit) 1

Plugging in the values, we get:

81 - 50 1 32

Therefore, the total number of possible events is 32.

Calculating the Probability

With the count of successful events and the total number of events, we can now calculate the probability:

Probability (Number of successful events) / (Total number of events)

Substituting the values, we get:

Probability 10 / 32 5 / 16

This means that if you randomly pick a number between 50 and 81, the probability that it will be a multiple of 2 greater than 60 is 5/16.

Loading Example for Greater Clarity

Let's consider a practical scenario. If you were to play a game where a number between 50 and 81 is randomly selected, and the player wins only if the number is a multiple of 2 greater than 60, the probability of winning would be 5/16. This can be understood through the following analogy:

If you're flipping a coin, the probability of getting heads or tails is 1/2. Similarly, the probability of picking a multiple of 2 greater than 60 from the range 50 to 81 is 5/16.

Conclusion

Understanding probability calculations, especially when dealing with ranges and specific conditions, is crucial. In this example, the range from 50 to 81 with the condition that the number must be a multiple of 2 greater than 60, the probability is determined to be 5/16. This knowledge not only enhances your mathematical skills but also aids in real-life situations where probability plays a crucial role.

Key Takeaways

Every even number is a multiple of 2. Total number of integers in a range (Upper limit - Lower limit) 1. Probability (Number of successful events) / (Total number of events).