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A probability experiment is conducted in which the sample space of the experiment is:

a) All possible outcomes
b) Only favorable outcomes
c) Only unfavorable outcomes
d) None of the above

User Kyle Baker
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Final answer:

The sample space in a probability experiment is the set of all possible outcomes. For instance, rolling a die followed by tossing a coin would have outcomes like '1 and heads' or '6 and tails'. The correct answer to what a sample space is would be 'All possible outcomes'.

Step-by-step explanation:

The sample space of an experiment is defined as the set of all possible outcomes of that experiment. For example, if the experiment is tossing a coin, the sample space would contain two outcomes: heads and tails. When dealing with sample spaces, we can define certain subsets of outcomes, called events, which may include things like getting a specific number of heads when tossing the coin multiple times. In probability, events are associated with a probability value between 0 and 1, indicating how likely they are to occur. An event with a probability of 1 always happens, while an event with a probability of 0 never happens.

To illustrate the concept with a compound experiment, consider rolling a die followed by tossing a coin. The sample space for this combined activity is all the possible combinations of die rolls and coin tosses, like rolling a 1 followed by getting heads, or rolling a 6 followed by getting tails. So, the correct answer to the question about what constitutes a sample space is option 'a': All possible outcomes.

User Nasly
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