A random number generator produces numbers between 1 and 99. If the current value of the random variable is 45, then what is the probability that the next randomly generated value for the same random variable, will also be 45. Explain clearly.
The Correct Answer and Explanation is:
In this scenario, the random number generator produces numbers between 1 and 99, meaning each number has an equal likelihood of being generated. This is a discrete uniform distribution where each number from 1 to 99 is equally probable.
The question asks about the probability that the next randomly generated number will also be 45, given that the current value is 45. The key here is that each draw from the random number generator is independent. The outcome of the previous draw does not affect the next draw. This is a fundamental property of random processes known as independence.
To explain clearly:
- The random number generator has 99 possible outcomes (numbers from 1 to 99).
- The probability of any specific number, including 45, being generated on any given draw is 199\frac{1}{99}991, because there are 99 equally likely outcomes.
- The previous value being 45 does not influence the next value. The system resets after each draw, meaning the number generated in the next step still has an equal chance of being 45, regardless of the previous number.
Thus, the probability that the next value will be 45 is simply 199\frac{1}{99}991.
Conclusion:
The probability that the next number generated will also be 45 is 199\frac{1}{99}991, which is approximately 0.0101 or 1.01%. This probability remains constant regardless of the previous number generated, due to the independence of the draws.
