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Likelihood represents the chance or probability of an event happening. It is commonly expressed as a number between 0 and 1. In this case, the likelihood of the last digit of a randomly generated phone number being zero is 1 in 10. This means that out of 10 phone numbers generated, one would expect, on average, that 1 of these numbers ends in zero.

To express likelihood as a probability value, we use the formula:
\ Probability = \( \frac{Number of Successful Outcomes}{Total Number of Possible Outcomes} \)

Here, the number of successful outcomes (a zero at the end of the phone number) is 1, and the total number of possible outcomes (which could be any digit from 0 to 9) is 10. The likelihood or probability is then calculated by dividing these numbers, giving us a probability of 0.1.

Random generation refers to the process of producing random outcomes, which in this context is randomly generating the last digit of a phone number. This means each digit (0-9) has an equal chance of being selected.

When a computer is used to generate a random digit, it simulates an unbiased process where each digit is equally likely. Therefore, the expected distributions of digits over many repetitions will be approximately even. Each digit would appear about ten percent of the time. This basis ensures fairness in scenarios needing random selection, like lotteries or surveys.

The principle behind this is simple: if a computer randomly picks one of the 10 digits, each digit (including zero) has a probability of \( \frac{1}{10} \). This characteristic is central to understanding randomness and how random numbers are used in probability.

Decimal fractions are another way to represent probabilities. In the provided example, the likelihood that the randomly generated last digit is zero can be expressed as the fraction \( \frac{1}{10} \).

To convert this fraction into a decimal fraction, you divide the numerator (1) by the denominator (10), which equals 0.1. Therefore, the probability that the last digit is zero is 0.1. This decimal represents the same probability but in a different format, making it easier to grasp and use for further calculations.

To summarize:

• The chance of an event happening (in this case, the last digit being zero) is first expressed as a fraction: \( \frac{1}{10} \).
• This fraction is then converted into a decimal by dividing the numerator by the denominator.
• The result is 0.1, which is a straightforward decimal fraction representing the same probability.

This conversion helps in interpreting and using probabilities across different contexts, such as performing calculations or comparing likelihoods.