Periodically, the Federal Trade Commission (FTC) monitors the pricing accuracy of electronic checkout scanners at stores to ensure consumers are charged the correct price at checkout. A study of over 100,000 items found that the probability that an item is priced incorrectly by the scanner is .03. (Price Check II: A Follow-Up Report on the Accuracy of Checkout Scanner Prices, Dec 16, 1998). Suppose the FTC randomly selects five items at a retail store and checks the accuracy of the scanner price of each. Let x represent the number of the five items that is priced incorrectly. a. What is the probability that exactly one of the five items is priced incorrectly by the scanner? b. What is the probability that at least one of the five items is priced incorrectly by the scanner? c. What is the probability that fewer than three of the five is priced incorrectly by the scanner?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
2. Periodically, the Federal Trade Commission (FTC) monitors the pricing accuracy of electronic
checkout scanners at stores to ensure consumers are charged the correct price at checkout. A
study of over 100,000 items found that the
scanner is .03. (Price Check II: A Follow-Up Report on the Accuracy of Checkout Scanner Prices,
Dec 16, 1998). Suppose the FTC randomly selects five items at a retail store and checks the
accuracy of the scanner price of each. Let x represent the number of the five items that is
priced incorrectly.
a. What is the probability that exactly one of the five items is priced incorrectly by the
scanner?
b. What is the probability that at least one of the five items is priced incorrectly by the
scanner?
c. What is the probability that fewer than three of the five is priced incorrectly by the
scanner?
It is given that the variable X represents the number of five items are incorrectly priced.
X follows Binomial distribution with n as 5 and p as 0.03.
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