ing 21. 15! 22. 2! 13! 4! 5! re an 23-40: Counting Methods. Answer the following questions us- ing the appropriate counting technique, which may be either arrangements with repetition, permutations, or combinations. Be sure to explain why this counting technique applies to the problem. ne is How 23. How many different nine-digit ZIP codes can be formed? 24. How different six-character passwords can be formed from the lowercase letters of the alphabet? many e (or is 25. How many different six-character passwords can be formed from the lowercase letters of the alphabet if repetition is not n your ny allowed? 26. A city council with eight members must elect a three-person executive committee consisting of a mayor, secretary, and n our 27. How many ways can the eight performances at a piano recital be ordered? ny treasurer. How many executive committees are possible? layers hope 28. A city council with ten members must appoint a four-person Low many subcommittees are possible? b) Find the expected value to me for this game expressed in a sentence. Chapter 7E Problems (textbook pages 465-466) Be certain to review the sample problems - in these problems I demonstrate how to reason out the answers to these questions. You do not need to know the formulas on pages 459 and 461 and I will not answer questions about these formulas. You need to read carefully and decide whether repeats are allowed and whether order matters. That's all you need to do to get the correct numerical solution to these problems. Please be sure to calculate the actual value of the response – do not leave numbers with exponents or use scientific notation. 24, 26, 40 Simply answer the question in the Problem. These answers are not probabilities. 44 Be sure to answer each question asked. These answers are not probabilities 50,52 Follow the directions in blue before problem 47 – use five significant digits in your answer. These answers are probabilities! MacBook Air F1 F2 F3 F4 F5 F6 F7 F8 F9 %23 %24 8. %24
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.
Question 24
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