Binomial Distribution and Bernoulli Trials

What is the condition for Bernoulli trials where the probability of success and failure remains constant?

What is the probability of failure in a Bernoulli trial?

What is the number of trials in a Binomial distribution?

What is the probability of getting exactly two people alive at age 65 years in the mortality example?

What is the characteristic of a Binomial random variable?

What is the name of the coefficient that represents choosing r from n without considering the order?

Binomial Coefficients

Binomial coefficients are the same as nCr, representing the number of ways to choose r items from a set of n items without considering the order.

Bernoulli Trials

A Bernoulli trial is a repeated experiment that satisfies three conditions: • Each trial has two possible outcomes: Success (S) and Failure (F) • The trials are independent • The probability of Success (and Failure) is constant for each trial

Binomial Distribution

A Binomial Distribution is the probability distribution for the number of successes in a sequence of Bernoulli trials
A Binomial Random Variable has: • n identical trials • Two outcomes: Success (S) and Failure (F) • Probability of Success: P(S) = p • Probability of Failure: P(F) = q = 1 – p • x is the number of Successes in n trials

Binomial Distribution Question

Mortality example: • Probability of a 20-year-old person being alive at 65 years: 80% (p = 0.8, q = 0.2) • Find the probability that the number alive at 65 years will be:
- Exactly two
- At most one
- At least one • Determine the probability distribution of the number alive at 65

Test your understanding of binomial distribution, binomial coefficients, and Bernoulli trials. Determine the value of each binomial coefficient and learn about the conditions of Bernoulli trials.