Binomial Probability

Front

What is the Binomial Probability Formula?

Back

P(X = k) = (nCk) * (p^k) * (q^(n-k)), where n = number of trials, k = number of successes, p = probability of success, q = probability of failure.

Front

What does 'n' represent in the binomial probability formula?

Back

The number of trials.

Front

What does 'k' represent in the binomial probability formula?

Back

The number of successes.

Front

What is a Binomial Distribution?

Back

A probability distribution that summarizes the likelihood that a value will take on one of two independent outcomes under a given set of parameters.

Front

What are the assumptions of a Binomial Distribution?

Back

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

Front

If a coin is tossed 10 times, what is the probability of getting exactly 6 heads?

Back

20.51%.

Front

What is the probability of getting exactly 10 heads when flipping a coin 20 times?

Back

17.62%.

Front

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

Back

Use the binomial probability formula: P(X = k) = (nCk) * (p^k) * (q^(n-k)).

Front

What is the value of 'p' in a fair coin toss?

Back

0.5 (the probability of getting heads).

Front

What is the value of 'q' in a fair coin toss?

Back

0.5 (the probability of getting tails).