In a randomly generated list of numbers from 0 to 6, what is the chance that each number will occur?A.B.C.D.SUBMITarrow_backPREVIOUS

Understanding the Problem

We need to determine the probability that each number from 0 to 6 occurs at least once in a randomly generated list of numbers.

Relevant Concepts

1. Sample Space: The total possible outcomes when generating numbers from 0 to 6.
2. Probability Calculation: The probability of an event occurring is calculated as: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

Analysis

1. Total Numbers: The numbers generated range from 0 to 6, which gives us 7 possible outcomes.
2. Event Definition: Each number (0, 1, 2, 3, 4, 5, 6) must occur at least once.
3. Random List Generation: Depending on the number of times we generate numbers in the list, we must analyze how the combinations work.

Verification

If the length of the generated list is less than 7, it's impossible for each number to occur since there aren’t enough slots to include each unique number. If at least 7 numbers are drawn, the chances of each occurring at least once increases. For simplicity, if the list is very large, we assume eventually all numbers will appear due to the law of large numbers.

Final Answer

The actual calculation of the exact probabilities would depend on the length of the list and whether repetitions are allowed. In a sufficiently long list, the chance tends toward certainty that all numbers (0 to 6) will eventually appear. However, without specific details on the list length, we can only conclude generally that the probability increases with more numbers drawn.