Binomial Probability Practice

Front

What is the formula for calculating 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

Define '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, p, is the same for each trial.

Front

What does 'n choose k' represent in binomial probability?

Back

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

Front

If a fair coin is flipped 10 times, what is the probability of getting exactly 5 heads?

Back

P(X = 5) = (10 choose 5) * (0.5)^5 * (0.5)^(10-5) = 0.2461.

Front

What is the expected value in a binomial distribution?

Back

The expected value (mean) of a binomial distribution is given by E(X) = n * p, where n is the number of trials and p is the probability of success.

Front

Explain the concept of 'success' in a binomial experiment.

Back

In a binomial experiment, 'success' refers to the outcome of interest that we are measuring, which can vary depending on the context of the experiment.

Front

What is the variance of a binomial distribution?

Back

The variance of a binomial distribution is given by Var(X) = n * p * (1 - p), where n is the number of trials and p is the probability of success.

Front

Calculate the probability of getting at least 3 heads when flipping a coin 5 times.

Back

P(X >= 3) = 1 - P(X < 3) = 1 - (P(X=0) + P(X=1) + P(X=2)) = 0.5.

Front

What is the probability of rolling a sum of 7 with two dice?

Back

The probability of rolling a sum of 7 with two dice is 6/36 = 1/6.

Front

Define 'independent events' in probability.

Back

Independent events are two or more events where the occurrence of one event does not affect the occurrence of the other.