Which of the following scenarios fits the condition of a $Bernoulli$ process?

• A. Flipping a fair coin $10$ times and recording whether each flip is heads or tails
• B. Measuring the exact height of each student in a class
• C. Selecting a card from a deck, not replacing it, and repeating the process
• D. Rolling a die and recording the number that appears each time

Answer: (A)

Verified step by step guidance

1. Understand the definition of a Bernoulli process: it is a sequence of independent trials where each trial has exactly two possible outcomes (often called 'success' and 'failure'), and the probability of success remains constant across trials.
2. Analyze the first scenario: flipping a fair coin 10 times. Each flip has two outcomes (heads or tails), the flips are independent, and the probability of heads (success) is constant at 0.5. This fits the Bernoulli process definition.
3. Consider the second scenario: measuring the exact height of each student. This is a continuous measurement, not a binary outcome, so it does not fit the Bernoulli process.
4. Look at the third scenario: selecting a card from a deck without replacement. The trials are not independent because the composition of the deck changes after each draw, so this is not a Bernoulli process.
5. Examine the fourth scenario: rolling a die and recording the number. Each trial has six possible outcomes, not two, so it does not meet the Bernoulli process criteria.