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

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

Back

P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where (n choose k) = n! / (k!(n-k)!).

Front

If p = 0.82, what is q?

Back

q = 1 - p = 0.18.

Front

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

Back

P(X = 4) = (5 choose 4) * (0.5)^4 * (0.5)^(5-4) = 5 * 0.0625 * 0.5 = 0.15625 or 15.625%.

Front

How do you find the probability of getting at least k successes?

Back

To find the probability of getting at least k successes, sum the probabilities of getting k, k+1, ..., n successes: P(X >= k) = Σ P(X = i) for i = k to n.

Front

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

Back

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

Front

What is the variance of a Binomial Distribution?

Back

The variance of a Binomial Distribution is Var(X) = n * p * (1 - p).

Front

In a survey, if 25% of bulbs are spoilt, what is the probability of exactly 3 spoilt bulbs out of 10?

Back

P(X = 3) = (10 choose 3) * (0.25)^3 * (0.75)^(10-3) = 0.250.

Front

What is the probability of having 8 good bulbs if 25% are spoilt?

Back

P(X = 8) = (10 choose 8) * (0.75)^8 * (0.25)^(10-8) = 0.2816.