Binomial Distribution - Math 4

Front

What is a Binomial Experiment?

Back

A binomial experiment is a statistical experiment that has the following properties: 1) The experiment consists of n identical trials. 2) Each trial has two possible outcomes: success or failure. 3) The probability of success, denoted by p, is the same for each trial. 4) The trials are independent.

Front

What are the conditions for a binomial distribution?

Back

1) Fixed number of trials (n). 2) Two possible outcomes (success or failure). 3) Constant probability of success (p) for each trial. 4) Independent trials.

Front

Is rolling a die ten times a binomial experiment?

Back

No, because there are more than two outcomes (1, 2, 3, 4, 5, 6).

Front

Is flipping a coin 20 times and counting heads a binomial experiment?

Back

Yes, because there are two outcomes (heads or tails) and the trials are independent.

Front

What is the probability of getting at least 2 successes in a binomial distribution?

Back

To find the probability of at least k successes, calculate 1 minus the probability of getting fewer than k successes.

Front

What is the formula for the 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 in binomial probability?

Back

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

Front

What is the mean of a binomial distribution?

Back

The mean (expected value) of a binomial distribution is given by μ = n * p.

Front

What is the variance of a binomial distribution?

Back

The variance of a binomial distribution is given by σ² = n * p * (1 - p).

Front

If the probability of success is 0.11 and there are 10 trials, what is the mean?

Back

Mean = n * p = 10 * 0.11 = 1.1.