Bernoulli 2 Do these situations involve Bernoulli trials?...

Bernoulli 2 Do these situations involve Bernoulli trials? Explain. a) You are rolling 5 dice and need to get at least two 6 's to win the game. b) We record the distribution of eye colors found in a group of 500 people. c) A manufacturer recalls a doll because about $3 \%$ have buttons that are not properly attached. Customers return 37 of these dolls to the local toy store. Is the manufacturer likely to find any dangerous buttons? d) A city council of 11 Republicans and 8 Democrats picks a committee of 4 at random. What's the probability they choose all Democrats? e) A 2002 Rutgers University study found that $74 \%$ of high school students have cheated on a test at least once. Your local high-school principal conducts a survey in homerooms and gets responses that admit to cheating from 322 of the 481 students.

Bernoulli 2 Do these situations involve Bernoulli trials? Explain.
a) You are rolling 5 dice and need to get at least two 6 's to win the game.
b) We record the distribution of eye colors found in a group of 500 people.
c) A manufacturer recalls a doll because about $3 \%$ have buttons that are not properly attached. Customers return 37 of these dolls to the local toy store. Is the manufacturer likely to find any dangerous buttons?
d) A city council of 11 Republicans and 8 Democrats picks a committee of 4 at random. What's the probability they choose all Democrats?
e) A 2002 Rutgers University study found that $74 \%$ of high school students have cheated on a test at least once. Your local high-school principal conducts a survey in homerooms and gets responses that admit to cheating from 322 of the 481 students.

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Key Concepts

Bernoulli Trials

A Bernoulli trial is an experiment where there are exactly two possible outcomes, commonly labeled as 'success' and 'failure.' For an experiment to qualify as a Bernoulli trial, each trial must be independent of the others and have a constant probability of success. This concept is foundational in probability theory and is used to model situations where each test or observation has a binary outcome.

Binomial Experiment

A binomial experiment is a sequence of independent Bernoulli trials conducted under identical conditions where the interest lies in counting the number of successes over a fixed number of trials. The binomial distribution, which arises from such experiments, provides the probabilities of obtaining a specific number of successes, making it a critical tool in statistical inference and decision-making.

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