Algebra 2 9.6 Binomial Distributions

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 (n) and the probability of success (p).

Front

What are the key characteristics of a Binomial Distribution?

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

Front

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

Back

P(X = k) = (nCk) * (p^k) * (q^(n-k)), where q = 1 - p.

Front

What does nCk represent in the Binomial formula?

Back

nCk, or 'n choose k', represents the number of combinations of n items taken k at a time.

Front

If a test has 10 questions and the probability of getting a question correct is 0.8, what is the probability of getting exactly 8 questions correct?

Back

P(X = 8) = (10C8) * (0.8^8) * (0.2^2) = 0.301.

Front

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

Back

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

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What is the variance of a Binomial Distribution?

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The variance is calculated as Var(X) = n * p * q, where q = 1 - p.

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What is the difference between independent and dependent trials in a Binomial Distribution?

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Independent trials mean the outcome of one trial does not affect the outcome of another, while dependent trials mean the outcome of one trial influences the outcome of another.

Front

What is the probability of success in a Binomial Distribution?

Back

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

Front

What is the probability of failure in a Binomial Distribution?

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The probability of failure (q) is calculated as q = 1 - p.