Binomial Probability Distribution

Front

What is a Binomial Probability Distribution?

Back

A Binomial Probability Distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success.

Front

What are the parameters of a Binomial Distribution?

Back

The parameters of a Binomial Distribution are 'n' (the number of trials) and 'p' (the probability of success on each trial).

Front

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

Back

The probability of exactly k successes in n trials is calculated using the formula: P(X = k) = (n choose k) * p^k * (1-p)^(n-k).

Front

What does 'n choose k' mean in the context of Binomial Distribution?

Back

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

Front

If the probability of success is 0.25 and you conduct 10 trials, what is the probability of getting exactly 8 successes?

Back

Using the Binomial formula: P(X = 8) = C(10, 8) * (0.25)^8 * (0.75)^2 = 0.2816.

Front

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

Back

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

Front

In a Binomial Distribution, what does the variance represent?

Back

The variance of a Binomial Distribution measures the spread of the distribution and is calculated as Var(X) = n * p * (1 - p).

Front

What is the relationship between Binomial Distribution and Bernoulli Trials?

Back

A Binomial Distribution is the sum of a fixed number of independent Bernoulli trials, where each trial has two possible outcomes: success or failure.

Front

How do you find the expected number of successes in a sample?

Back

To find the expected number of successes in a sample, multiply the total number of trials (n) by the probability of success (p).

Front

What is the probability of getting 4 tails when tossing a coin 5 times?

Back

Using the Binomial formula: P(X = 4) = C(5, 4) * (0.5)^4 * (0.5)^1 = 0.15625 or 15.625%.