Probability
how likely something is to happen
1. What is probability?
Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
2. How do we calculate probability?
Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability approach.
Another approach is the empirical probability, which involves conducting a series of trials and calculating the ratio of the number of times an event occurs to the total number of trials.
Finally, there is the subjective probability approach, which involves making an educated guess based on personal experience, knowledge, and intuition.
3. What is the difference between dependent and independent events?
In probability, events can either be dependent or independent. An independent event is one where the outcome of one event does not affect the outcome of the other event. For example, if you flip a coin twice, the outcome of the first flip does not affect the outcome of the second flip.
On the other hand, dependent events are those where the outcome of one event affects the outcome of the other. For example, drawing a card from a deck and not replacing it changes the probability of drawing another card and affects the probability of the next event.
4. What is the difference between permutation and combination?
Both permutation and combination are methods to solve problems that involve counting the number of possible outcomes.
Permutation is an ordered arrangement of objects. Permutation formula is n!/(n-r)!, where n is the total number of objects, and r is the number of objects selected.
Combination, on the other hand, is an unordered selection of objects. Combination formula is n!/(r!(n-r)!), where n is the total number of objects, and r is the number of objects selected.
5. What is the law of large numbers?
The law of large numbers states that as the number of trials increases, the empirical probability approaches the theoretical probability. This means that over a large number of trials, the actual results will converge towards the expected results.
More Answers:
The Sample Space In Probability Theory: Definition And Examples.Probability Theory: Calculating Probability Of Non-Mutually Exclusive Events
Master The Art Of Combinations: The Concepts And Formulas For Mathematics, Probability, Combinatorics, And Set Theory