Probability Questions

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, expressed as a number between 0 and 1.

Front

What is the formula for calculating the probability of a single event?

Back

P(A) = Number of favorable outcomes / Total number of possible outcomes.

Front

What does it mean if an event has a probability of 0?

Back

It means that the event is impossible and will not occur.

Front

What does it mean if an event has a probability of 1?

Back

It means that the event is certain to occur.

Front

What is the complement of an event?

Back

The complement of an event A is the event that A does not occur, denoted as A'. The probability of the complement is P(A') = 1 - P(A).

Front

What is a binomial distribution?

Back

A binomial distribution is a probability distribution that summarizes the likelihood that a value will take one of two independent states and is defined by the number of trials and the probability of success.

Front

What is the Poisson distribution used for?

Back

The Poisson distribution is used to model the number of times an event occurs in a fixed interval of time or space.

Front

How do you calculate the probability of getting exactly k successes in n trials in a binomial distribution?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where p is the probability of success.

Front

What is the expected value in probability?

Back

The expected value is the long-term average of a random variable, calculated as E(X) = Σ [x * P(x)], where x is a possible outcome and P(x) is its probability.

Front

What is the law of large numbers?

Back

The law of large numbers states that as the number of trials increases, the experimental probability of an event will converge to its theoretical probability.