Probability
A — of any outcome of a random process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long series of trials.
1. What is probability?
Probability refers to the likelihood of an event occurring, expressed as a number between 0 and 1. A probability of 0 indicates that the event will not occur, while a probability of 1 indicates that the event is certain to occur.
2. What is the difference between theoretical probability and experimental probability?
Theoretical probability is the probability of an event that is calculated based on a theoretical model or mathematical formula. It is an idealized concept that assumes that all possible outcomes are equally likely. Experimental probability, on the other hand, is the probability of an event that is determined by conducting an actual experiment or observation. It is based on the actual results of the experiment, and may differ from theoretical probability when actual outcomes are not equally likely.
3. What is the Law of Large Numbers?
The Law of Large Numbers is a statistical principle that states that as the sample size increases, the average of the sample approaches the expected value of the population. In other words, the more data we collect, the closer we get to the true probability. This principle is important in statistics because it allows us to make accurate predictions based on a large sample size.
4. What is Bayes’ Theorem?
Bayes’ Theorem is a formula for calculating conditional probability. It is used to update the probability of an event occurring based on new information or evidence. The formula is P(A|B) = P(B|A) P(A) / P(B), where P(A) is the prior probability of event A, P(B) is the total probability of event B occurring, and P(B|A) is the probability of event B given that event A has occurred.
5. What are independent events?
Independent events are events that do not affect each other’s probability of occurring. In other words, the probability of one event occurring does not change based on the occurrence or non-occurrence of the other event. For example, the probability of flipping a coin and getting heads is independent of the probability of rolling a dice and getting a 6.
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