Equally Likely Events:
In an experiment, if one outcome cannot be expected to occur in preference to the other, the events are said to be equally likely. This means that all possible outcomes have an equal chance of occurring. For example, flipping a fair coin has two equally likely outcomes - heads or tails.

Explanation:
When we conduct an experiment, we are interested in the different outcomes that can occur. These outcomes are known as events. In some experiments, the outcomes may have different probabilities of occurring. However, in other cases, the outcomes may have the same probability of occurring. When the outcomes have the same probability, they are considered equally likely events.

For example, consider rolling a fair six-sided die. Each face of the die has an equal chance of landing face up. Therefore, the outcomes of rolling the die are equally likely events. Each outcome - 1, 2, 3, 4, 5, and 6 - has a probability of 1/6 of occurring.

Similarly, consider drawing a card from a well-shuffled deck of 52 cards. Each card in the deck has an equal chance of being drawn. Therefore, the outcomes of drawing a card from the deck are equally likely events. Each outcome - any of the 52 cards - has a probability of 1/52 of occurring.

In both of these examples, no outcome can be expected to occur in preference to the others because they all have the same probability. Therefore, the events are equally likely.

Conclusion:
When conducting an experiment, if the outcomes of the experiment have the same probability of occurring, they are considered equally likely events. This means that no outcome can be expected to occur in preference to the others. Equally likely events are important in probability theory as they help us calculate the probabilities of different outcomes and make predictions based on those probabilities.