(MMC Exercises 4.1) Are these phenomena random? Identify each of the following phenomena as random or not. Give reasons for your answers. a. You roll a six-sided die that has one to six spots on each side. b. The last digit of your phone number. You draw a 10 from a well-shuffled deck of 52 cards. d. Your date of birth.
The Correct Answer and Explanation is :
Identifying Random Phenomena
Let us evaluate whether each phenomenon is random, explaining the reasoning for each.
a. Rolling a six-sided die
Random:
Rolling a six-sided die is a random phenomenon because the outcome is uncertain and depends on chance. When a fair die is rolled, each side (numbered 1 through 6) has an equal probability of landing face up, and the outcome cannot be predicted in advance. The die is designed to ensure that each face has a ( \frac{1}{6} ) probability, assuming it is unbiased and rolled under standard conditions.
b. The last digit of your phone number
Not random:
The last digit of your phone number is not a random phenomenon because it was assigned or chosen and does not change unpredictably. Phone numbers are typically assigned based on a systematic process by telecommunication providers, often following regional or numerical patterns. While the digit might appear random at a glance, it is deterministic in its assignment.
c. Drawing a 10 from a well-shuffled deck of 52 cards
Random:
Drawing a card from a well-shuffled deck is a random phenomenon. After the deck is shuffled, the arrangement of cards is unpredictable, and each card has an equal likelihood of being drawn. For example, there are four 10s in a standard deck, so the probability of drawing a 10 is ( \frac{4}{52} ), or approximately 7.69%. The randomness depends on proper shuffling to ensure all cards are equally likely to appear.
d. Your date of birth
Not random:
Your date of birth is not a random phenomenon because it is a fixed fact based on when you were born. While the distribution of birthdays across a population might show some patterns, an individual’s date of birth does not change and is determined by specific historical and biological circumstances.
Conclusion:
Phenomena like rolling dice or drawing cards involve inherent uncertainty, qualifying as random events. In contrast, assigned or predetermined phenomena like phone numbers or dates of birth are deterministic and not random. This distinction helps us understand when probability and randomness apply in analyzing outcomes.