Binomial Distribution

Front

What is a Binomial Distribution?

Back

A Binomial Distribution is a probability distribution that summarizes the likelihood of a value taking on two independent outcomes, typically referred to as 'success' and 'failure', over a fixed number of trials.

Front

What are the assumptions of a Binomial Distribution?

Back

1. The number of trials (n) is fixed. 2. Each trial is independent. 3. Each trial has only two possible outcomes (success or failure). 4. The probability of success (p) is constant for each trial.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What does 'n' represent in a Binomial Distribution?

Back

'n' represents the number of trials or experiments conducted.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What does 'p' represent in a Binomial Distribution?

Back

'p' represents the probability of success on a single trial.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What is the formula for calculating the probability of exactly k successes in n trials?

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n! / (k!(n-k)!)

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

How do you denote the probability of getting at least k successes?

Back

P(X ≥ k) = 1 - P(X < k) = 1 - ∑(P(X = i) for i = 0 to k-1).

Front

What is the probability of getting exactly 3 heads in 5 coin flips?

Back

Using the Binomial formula: P(X = 3) = (5 choose 3) * (0.5)^3 * (0.5)^(5-3) = 10 * 0.125 * 0.25 = 0.3125.

Tags

CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

Front

What is the expected value (mean) of a Binomial Distribution?

Back

The expected value (mean) is given by E(X) = n * p.

Tags

CCSS.HSS.MD.A.2

Front

What is the variance of a Binomial Distribution?

Back

The variance is given by Var(X) = n * p * (1 - p).

Front

What is the standard deviation of a Binomial Distribution?

Back

The standard deviation is the square root of the variance: SD(X) = √(n * p * (1 - p)).