Probability: Definition, Calculation, Distribution, And Theorems.

Probability

(the number of successes) / (the total number of possibilities)

1. What is the definition of probability?

Probability is a branch of mathematics that deals with the study of random events, and the likelihood of their occurrence or non-occurrence.

2. How do you calculate probability?

Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes. The probability of an event occurring ranges from 0 to 1, or from 0% to 100%.

3. What is the difference between theoretical and experimental probability?

Theoretical probability is the probability of an event based on mathematical analysis, whereas experimental probability is the probability of an event based on actual data collected from observations or experiments.

4. What is a probability distribution?

A probability distribution is a function that describes the likelihood of different outcomes in a random experiment or process. It assigns a probability to each possible outcome, and the sum of all probabilities equals 1.

5. What is the difference between discrete and continuous probability distribution?

Discrete probability distribution deals with events that have a finite or countable number of possible outcomes, such as the number of heads in a coin toss. Continuous probability distribution deals with events that have an infinite number of possible outcomes, such as the height of people in a certain population.

6. What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. It is represented as P(A|B), where A and B are two events, and | means “given”.

7. What is Bayes’ theorem?

Bayes’ theorem is a mathematical formula that describes the probability of an event based on prior knowledge or evidence. It is given by P(A|B) = P(B|A) * P(A) / P(B), where A and B are two events, and P(A), P(B), P(B|A), and P(A|B) are their probabilities.

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