5.3 CPS Oswego High School

A probability distribution that results from a procedure with a fixed number of independent trials, where each trial has two possible outcomes (success or failure), and the probability of success remains constant for each trial.

A characteristic of a binomial distribution; the total number of trials in the procedure is predetermined and unchanging.

In a binomial distribution, the outcome of one trial does not affect the outcome of any other trial. If the sample size is less than 5% of the population, it's often treated as independent.

Each trial in a binomial distribution must have exactly two mutually exclusive outcomes, often labeled as 'success' (S) and 'failure' (F).

The probability of achieving a 'success' (S) must remain consistent across all trials in a binomial distribution.

Represents the probability of success in a single trial.

Represents the probability of failure in a single trial. Calculated as 1 - p.

Represents the fixed number of trials in a binomial experiment.

Represents a specific number of successes in n trials. It can range from 0 to n.

Describes the probability of getting a certain number of successes in a fixed number of independent trials, where each trial has the same probability of success.

The likelihood of a single trial resulting in a desired outcome.

The likelihood of a single trial not resulting in the desired outcome.

The total number of independent experiments or observations.

The specific number of desired outcomes in the total trials.

P(x) = nCx * p^x * q^(n-x), where nCx is the combination of choosing x successes from n trials.

Calculator function for finding the probability of exactly x successes in n trials with probability of success p.

Calculator function to find the probability of x or fewer successes in n trials with probability p.

Events that do not affect the probability of future events.

The probability of an event happening less than 6 times in 20 trials, with a 0.5 probability of success in each trial, calculated using binomial cumulative distribution function.

The probability of getting 14 or more heads when tossing a coin 32 times, calculated using the complement rule and the binomial cumulative distribution function.

The likelihood of precisely one person in a class of 25 being allergic to bee stings, given a 1% allergy rate, calculated using the binomial probability density function.

The probability that 4 or more people in a class of 25 are allergic to bee stings, calculated using the complement rule and the binomial cumulative distribution function.

Calculating the probability of finding exactly five students receiving financial aid in a group of nine students, given a 53% financial aid rate.

The probability that fewer than three students in a group of nine receive financial aid, using the binomial cumulative distribution function.

Checking if a procedure fits a binomial distribution by verifying pre-defined conditions, and identifying criteria not met if necessary.

Identifying n, x, p, and q components of a binomial distribution in a given scenario.

Checking if procedure generates binomial distribution, considering fixed number of trials, independence, and unique outcomes.

Determining if a scenario fits a binomial distribution and explain why or why not.

In a binomial experiment, the outcome of any individual trial doesn't influence the outcome of other trials.

Method for calculating probability of obtaining a specific number of successes in a fixed number of independent trials.

Using pre-calculated tables to quickly find probabilities in binomial distribution.

Using the formula to find the probability of x successes given p and n in binomial distribution.

Using a supplied Minitab output or equivalent to determine binomial probabilities for specific n and p values.

The fixed number of trials in a binomial distribution.

The specific number of successes you are interested in during 'n' trials.

Probability of success in a single trial.

Probability of failure in a single trial.

The likelihood of finding at least one donor with Group O blood type in a sample, calculated as 1 minus the probability of finding zero donors with Group O blood type.

The probability of getting exactly 'k' successes in 'n' independent trials, each with the same probability of success 'p'.

Find the probability of getting less than 'k' successes in a binomial experiment.

Calculate the probability of getting 'k' or more successes in a binomial experiment.

The probability of observing a particular number of successes in a series of independent trials.

Percentage of people who recognize a particular brand.

The probability of finding at least three people who recognize McDonald's in a group of 5.

The chance of getting exactly 5 students who receive financial aid out of 9.

The probability of finding less than 3 students who receive financial aid.