Binomial Probability - Midterm Exam Review

Front

What is Binomial Probability?

Back

Binomial Probability is the probability of obtaining a fixed number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What is a Bernoulli trial?

Back

A Bernoulli trial is a random experiment where there are only two possible outcomes: success or failure.

Front

What is the formula for Binomial Probability?

Back

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

Front

What does 'n choose k' mean?

Back

'n choose k' (denoted as C(n, k) or nCk) is the number of ways to choose k successes from n trials, calculated as n! / (k!(n-k)!).

Front

What is the probability of at least one success?

Back

The probability of at least one success in n trials is calculated as 1 - P(X = 0).

Front

How do you calculate the probability of exactly k successes in n trials?

Back

Use the Binomial Probability formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k).

Front

What is the significance of the probability of success (p)?

Back

The probability of success (p) is the likelihood of achieving a successful outcome in a single trial.

Front

What is the complement rule in probability?

Back

The complement rule states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

Front

How do you find the probability of 'at least k successes'?

Back

To find the probability of at least k successes, sum the probabilities from k to n: P(X >= k) = P(X = k) + P(X = k+1) + ... + P(X = n).

Front

What is the expected value in a binomial distribution?

Back

The expected value (mean) of a binomial distribution is calculated as E(X) = n * p.