An event has a theoretical probability of 20%. Which of the following must be true?
Its experimental probability will always be 20%.
The experimental probability of its complement will always be 80%.
The theoretical probability of its complement will always be 80%.
The theoretical probability of its complement will always be -20%.
You can not say experimental probability will ALWAYS be the same. That is the thing about experiments.
The complement = 1 - p = 1 - .2 = .8
so I would pick
theoretical complement = 80%
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The correct answer is: The theoretical probability of its complement will always be 80%.
To understand why, we need to first define a few terms. Theoretical probability refers to the chance of an event occurring based on mathematical analysis or calculations. Experimental probability, on the other hand, is the probability of an event occurring based on actual experiments or observations.
In this case, the theoretical probability of the event is given as 20%. The complement of an event refers to the event not occurring. In other words, it is the probability of the opposite or negation of the event.
Since the theoretical probability of the event is 20%, the theoretical probability of its complement (the event not occurring) is 100% minus 20%, which is equal to 80%.
Hence, the correct statement is that the theoretical probability of its complement will always be 80%.
To determine which of the following statements must be true, we need to understand the relationship between theoretical probability, experimental probability, and complementary events.
Theoretical probability refers to the likelihood of an event occurring based on mathematical calculations. It is determined by dividing the number of favorable outcomes by the number of possible outcomes.
Experimental probability, on the other hand, is the likelihood of an event occurring based on actual observations or experiments. It is determined by dividing the number of times an event occurred by the total number of trials or observations.
Complementary events are two events that together cover all possible outcomes. The probability of an event and its complement always add up to one (or 100%).
Now, let's evaluate each statement:
1. Its experimental probability will always be 20%.
This statement cannot be guaranteed. Experimental probability is based on actual observations or experiments, and it can vary from the theoretical probability. Therefore, the experimental probability may or may not be 20%.
2. The experimental probability of its complement will always be 80%.
This statement also cannot be guaranteed. The experimental probability of the complement event, which consists of all outcomes not included in the original event, is not directly related to the theoretical probability. It will depend on the actual observations or experiments conducted.
3. The theoretical probability of its complement will always be 80%.
This statement cannot be true. The probability of an event and its complement must add up to one (or 100%). If the theoretical probability of an event is 20%, then the theoretical probability of its complement will be 1 - 0.20 = 0.80 or 80%.
4. The theoretical probability of its complement will always be -20%.
This statement cannot be true. Probability values are always non-negative. They represent the likelihood of an event occurring, and a negative probability is not meaningful or valid.
In conclusion, the correct answer is:
The theoretical probability of its complement will always be 80%.