In a recent year, it was estimated that 55% of U.S. adult...

In a recent year, it was estimated that 55$\%$ of U.S. adult Internet users had access to high-speed Internet connections at home or on the job. What is the probability that exactly 2 out of 5 randomly selected U.S. adults had access to high-speed Internet connections?

Key Concepts

Binomial Distribution

The binomial distribution is a probability distribution that describes the likelihood of achieving a fixed number of successes in a specified number of independent trials, where each trial has exactly two possible outcomes (commonly referred to as success and failure) and the probability of success remains constant throughout.

Bernoulli Trials

Bernoulli trials refer to experiments or processes that have exactly two mutually exclusive outcomes, usually labeled as success and failure. They serve as the foundational experiment in situations where the binomial distribution applies because each trial is independent and identically distributed.

Probability Mass Function

The probability mass function (PMF) of the binomial distribution is a formula used to calculate the probability of observing exactly a certain number of successes in a given number of Bernoulli trials. This function combines combinatorial principles and the probabilities of success and failure raised to the number of successes and failures, respectively.

Combinatorics

Combinatorics involves the counting of configurations or arrangements, which is integral to determining how many ways a set number of successes can occur in a sequence of trials. In the context of the binomial distribution, it assists in calculating the number of ways to choose a given number of trials to be successful from the total number of trials.

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