When none of the outcomes is favourable to the event then the event is...
The correct answer for the given question is option 'C', which states that when none of the outcomes is favorable to the event, the event is said to be impossible. Let's understand this concept in detail:
Introduction:
In probability theory, an event refers to a specific outcome or set of outcomes of an experiment or random phenomenon. The outcomes of an event can be classified into three categories: favorable, unfavorable, or impossible.
Explanation:
1. Favorable outcomes: These are the outcomes that meet the desired condition or criteria of the event. For example, if the event is "rolling a 6 on a fair six-sided die," the favorable outcome is rolling a 6.
2. Unfavorable outcomes: These are the outcomes that do not meet the desired condition or criteria of the event. Using the same example, the unfavorable outcomes would be rolling any number other than 6 (1, 2, 3, 4, or 5).
3. Impossible outcomes: When none of the outcomes satisfy the desired condition or criteria of the event, the event is said to be impossible. In other words, there are no possible outcomes that can occur for the given event.
Example:
Let's consider the event of rolling a 7 on a fair six-sided die. Since the maximum number that can be rolled on a six-sided die is 6, rolling a 7 is not possible. Therefore, the event of rolling a 7 is impossible.
Conclusion:
When none of the outcomes is favorable to the event, it indicates that the event cannot occur or is not possible. Hence, the correct answer is option 'C' - impossible.
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