Final answer:
The probability of randomly generating a particular four-digit PIN like '0005' is 1 out of 10,000, or 0.0001. The process of selecting random class members using random numbers involves reading two-digit groups to maintain fairness. The significance of digits and rounding rules are important in mathematical calculations.
Step-by-step explanation:
Understanding the Probability of a Personal Identification Number (PIN)
To find the probability that a personal identification number (PIN) consists of four digits and is equal to the number 5 (with consideration to PINs like 0005), we must understand the total number of possible PINs. Since each position in a 4-digit PIN can be any of the digits from 0 to 9, there is a total of 10 possibilities for each position. The total number of possible PINs is therefore 104 or 10,000. The PIN '0005' is just one of these possible combinations, so the probability of randomly generating this PIN is 1 out of 10,000, or 0.0001.
In terms of selecting random numbers for different purposes, such as Lisa choosing three class members using random two-digit numbers from a calculator, the process involves reading off two-digit numbers from the generated random decimals. This method ensures the randomness of selection. Each number contributes only one class member to maintain fairness and randomness in the selection process.
Understanding concepts like the significance of digits and rounding is important in various applications in mathematics, including in probability and statistics. For example, when rounding numbers, a digit 5 or above will round the previous digit up, while digits below 5 will not alter the previous digit.