Determine whether the given random variable has a binomial...

determine whether the given random variable has a binomial distribution. Justify your answer. 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.

determine whether the given random variable has a binomial distribution. Justify your answer.
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

Binomial Distribution

The binomial distribution models the number of successes in a predetermined fixed number of independent Bernoulli trials, where each trial has only two outcomes (success or failure) and the probability of success remains constant across trials. The key properties are that the number of trials is fixed and each trial is independent of the others.

Geometric Distribution

The geometric distribution describes the number of trials needed to achieve the first success in a series of independent Bernoulli trials with a constant probability of success. Unlike the binomial distribution, the number of trials is not predetermined but is instead a random variable that counts until the first occurrence of success.

Bernoulli Trials

Bernoulli trials are experiments or processes that result in a binary outcome (commonly denoted as success or failure), where the probability of success is the same in each trial and the trials are independent. They serve as the foundational building blocks for both the binomial and geometric distributions.

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