In Exercises 69 to 72, explain whether the given random...

In Exercises 69 to $72,$ explain whether the given random variable has a binomial distribution. Lefties Exactly 10$\%$ of the students in a school are left-handed. Select students at random from the school, one at a time, until you find one who is left-handed. Let $V=$ the number of students chosen.

In Exercises 69 to $72,$ explain whether the given random variable has a binomial distribution.

Lefties Exactly 10$\%$ of the students in a school are left-handed. Select students at random from the school, one at a time, until you find one who is left-handed. Let $V=$ the number of students chosen.

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Key Concepts

Bernoulli Trial

A Bernoulli trial is an experiment or process that produces one of two outcomes—commonly labeled as success or failure—with a fixed probability for success in each independent trial. This fundamental concept underlies both binomial and geometric distributions.

Binomial Distribution

A binomial distribution applies when there is a fixed number of independent trials, each trial has two possible outcomes (success or failure), and the probability of success remains constant across those trials. The random variable in such a distribution represents the number of successes in that fixed set of trials.

Geometric Distribution

A geometric distribution models the number of independent trials required to achieve the first success, with a constant probability of success on each trial. Unlike the binomial distribution, the number of trials is not predetermined but rather stops as soon as the first success is observed.

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