Which of the following situations cannot be described by a $discrete$ probability distribution?

• A. The number of heads obtained when flipping a coin three times
• B. The number of cars passing through a toll booth in one hour
• C. The number of students present in a classroom on a given day
• D. The exact height of a randomly selected adult measured in $cm$

Answer: (D)

Verified step by step guidance

1. Understand the definition of a discrete probability distribution: it describes the probabilities of outcomes that are countable, often integers, such as counts of events or objects.
2. Examine each situation to determine if the possible outcomes are countable (discrete) or continuous (can take any value within a range).
3. For 'the number of heads obtained when flipping a coin three times,' the outcomes are 0, 1, 2, or 3 heads, which are countable integers, so this is discrete.
4. For 'the number of cars passing through a toll booth in one hour,' the count of cars is a non-negative integer, so this is also discrete.
5. For 'the number of students present in a classroom on a given day,' the count is again a non-negative integer, making it discrete. However, 'the exact height of a randomly selected adult measured in centimeters' can take any value within a range and is not countable, so it cannot be described by a discrete probability distribution.