Define the following terms:
(i random experiments
(ii) sample space
(ili) mutualy exclusive events.

Here are definitions for the given terms:

1. **Random Experiments**: A random experiment is an action or process that leads to one of several possible outcomes, where the outcome cannot be predicted with certainty in advance. For example, tossing a coin is a random experiment because you cannot predict whether it will land on heads or tails.

2. **Sample Space**: The sample space of a random experiment is the set of all possible outcomes of that experiment. For instance, in the case of tossing a coin, the sample space is {Heads, Tails}. If rolling a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.

3. **Mutually Exclusive Events**: Mutually exclusive events are events that cannot happen at the same time. In other words, if one event occurs, the other cannot. For example, when rolling a die, the events "rolling a 3" and "rolling a 5" are mutually exclusive because you can't roll both a 3 and a 5 on a single roll.

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Would you like further details on any of these concepts? Here are some related questions to expand on these topics:

1. Can you give an example of a random experiment involving more than two outcomes?
2. How would you describe the sample space for drawing a card from a deck of 52 cards?
3. What is the probability of two mutually exclusive events occurring at the same time?
4. Can mutually exclusive events ever have non-zero probabilities?
5. How does the concept of mutually exclusive events differ from independent events?

**Tip**: When dealing with probability, always verify whether events are mutually exclusive or independent as this determines how you calculate their probabilities.

Define the following terms: (i) random experiments, (ii) sample space, (iii) mutually exclusive events.

Explore key probability concepts, including random experiments, sample space, and mutually exclusive events. This guide explains these fundamental ideas with examples, making it ideal for high school students studying probability theory.

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