Exploring Mobile Number Possibilities and Probability Distribution

With the proliferation of mobile communication technology, phone numbers have become part of our daily lives. A common question that often arises involves the format and probability of certain configurations of these numbers. In this article, we delve into the intricacies of a specific 11-digit mobile number format where the first two digits are 0 and 9, and we explore how many possible numbers fit this format. Additionally, we examine the probability of randomly selecting one of these mobile numbers whose last four digits in order are 2911.

Understanding the Format of Mobile Numbers

Let us consider a specific format of a 11-digit mobile number where the first two digits are 0 and 9. This format may vary depending on the country or region, but in this context, we focus on a hypothetical scenario where 09 appears at the beginning of the number.

Determining the Number of Possible Mobile Numbers

The last nine digits of the number can be any digit from 0 to 9. Since each digit has 10 possibilities, we calculate the total number of possible combinations as follows:

10^9 1,000,000,000

However, it is important to note that the calculation of (10^9) does not take into account the possibility of consecutive zeros. For instance, 000000000 is still counted in the total. Therefore, the total number of possible 11-digit mobile numbers starting with 09 and followed by nine more digits is still (10^9).

Considering the Order of the First Two Digits

It is crucial to consider the order of the first two digits, which are 0 and 9. If these digits do not need to be in order, then both 09 and 90 are valid. Multiplying the total number of combinations by 2 accounts for this:

Total possible numbers 2 x (10^9)

Probability of Selecting a Specific Sequence

We now turn to the probability of randomly selecting a mobile number whose last four digits are 2911. To do this, we will first determine the total number of possible mobile numbers in the format 09xxxxxxx and then calculate the probability.

As previously calculated, the total number of possible mobile numbers starting with 09 is:

Total possible numbers 2 x (10^9)

The probability of selecting a mobile number ending in 2911 is the ratio of the number of mobile numbers ending in 2911 to the total number of mobile numbers:

Probability (frac{1}{10^4})

Explanation of the Probability Calculation

Since the last four digits of a mobile number can be any combination of 0 to 9, there are (10^4 10,000) possible combinations for these four digits. Therefore, the probability of selecting a mobile number ending in 2911 is:

Probability (frac{1}{10^4} frac{1}{10000})

Given that the probability is quite low, it emphasizes the vastness of the number of possible mobile numbers, specifically those starting with 09. The calculation also highlights the importance of consideration in the initial digits when analyzing large sets of data or random selections.

Conclusion

In conclusion, the total number of possible mobile numbers in the format 09xxxxxxx is (2 times 10^9). The probability of randomly selecting a mobile number ending in 2911 is (frac{1}{10^4}). This analysis underscores the vast number of possible mobile numbers and the mathematical intricacies involved in their randomness and distribution.