Suppose 60 percent of all people prefer Coke to Pepsi. We...

Suppose 60 percent of all people prefer Coke to Pepsi. We select 18 people for further study.
a. How many would you expect to prefer Coke?
b. What is the probability 10 of those surveyed will prefer Coke?
c. What is the probability 15 prefer Coke?

Key Concepts

Combinatorial Analysis

Combinatorial analysis involves the calculation of combinations, often noted as 'n choose k'. This calculation is crucial in the binomial probability formula, as it determines the number of ways to select k successes from n trials. It is a fundamental tool in probability theory for counting the number of possible outcomes in a structured way.

Probability Mass Function

The probability mass function (PMF) for the binomial distribution gives the probability that a discrete random variable is exactly equal to a specific value. The PMF is given by the formula P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where k is the number of successes, providing a way to determine the likelihood of a particular outcome in a binomial scenario.

Expected Value

The expected value in a binomial setting is the mean number of successes in a given number of trials. It is calculated as n multiplied by p, where n is the total number of trials and p is the probability of success on each trial. This concept helps predict the average outcome over many repetitions of the experiment.

Binomial Distribution

The binomial distribution is a probability model used when there are a fixed number of independent trials, each resulting in a success or a failure, with the same probability of success in every trial. This concept is relevant for problems where outcomes like preference, response, or occurrence are in two possible categories, typically modeled with parameters n (number of trials) and p (probability of success).

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