Final answer:
A coin flip is a binomial scenario since it has two outcomes, while rolling a die is not binomial due to having more than two outcomes. Drawing a card from a deck or selecting a marble from a bag could potentially be modeled as binomial experiments if the outcomes are defined dichotomously.
Step-by-step explanation:
To understand which scenarios among the given options are binomial, we need to consider the definition of a binomial experiment. A binomial experiment has the following characteristics:
- There are a fixed number of trials.
- Each trial has two possible outcomes: a 'success' or a 'failure'.
- The probability of 'success' remains constant from trial to trial.
- The trials are independent of one another.
Now let's examine each scenario:
- Rolling a die is not binomial because there are more than two outcomes.
- Flipping a coin is a binomial scenario because there are two outcomes, 'head' or 'tail', which can be regarded as 'success' or 'failure'.
- Drawing a card from a deck is not binomial unless the problem is phrased in a binary context, like drawing a specific card versus not drawing that card.
- Selecting a marble from a bag can be binomial if the event is picking a specific color of marble versus any other color.
In the context provided, flipping a coin clearly fits the binomial criteria and selecting a marble could potentially be binomial depending on the particular conditions set for 'success'. However without those specific conditions, selecting a marble is initially not a binomial scenario.