# SECTION 3.1 Events, Sample Spaces, and Probability 131 ified according to de- -moderate, moderate, a. In how many possible ways can the three-grill displays be selected from the 5 displays? List the possibilities. measurements b. The next table shows the grill display combinations and number of each selected by the 124 students. Use this information to assign reasonable probabilities to the are re- One tooth is randomly is the probability that mount of wear? different display combinations. c. Find the probability that a student who participated in the study selected a display combination involving Grill #1. light ight Grill Display Combination Number of Students 35 42 eavy nworn 1-2-3 1-2-4 1-2-5 2-3-4 2-3-5 2-4-5 ght-moderate ght-moderate oderate 4 worn known 34 question posed in a meteorologist rnoon is .4," does time during the Based on Hamilton, R. W."Why do people suggest what they do not want? Using context effects to influence others' choices." Journal of Consumer Research, Vol. 29, Mar. 2003, Table 1. n he the Journal of 13) investigation y station with 11 gorithm designed is one in which tracks to a train 3.30 ESL students and plagiarism. The Journal of Education and Human Development (Vol. 3, 2009) investigated the causes of plagiarism among six English-as-a-second- language (ESL) students. All students in the class wrote two essays, one in the middle and one at the end of the semester. After the first essay, the students were in- structed on how to avoid plagiarism in the second essay. Of the six ESL students, three admitted to plagiarizing on the first essay. Only one ESL student admitted to plagia- rizing on the second essay. (This student, who also plagia- rized on the first essav, claimed she misplaced her notes s is assigned to an

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.

Refer to the study below of how people attempt to influence the choices of others. Recall that students selected three portable grill displays to be compared from an offering of five different grill displays.

a). Use a counting rule to count the number of ways the three displays can be selected from the five available displays to form a three grill display combination.

b). The researchers informed students to select the three displays in order to convince people to choose Grill #2. Consequently, Grill #2 was a required selection. Use a counting rule to count the number of different ways the three grill displays can be selected from the five displays if grill #2 is selected. (The answer should agree with the answer of a)

c). Now suppose the three selected grills will be set up in a specific order for viewing by a customer. (The customer views one grill first, then the second, and finally the third grill). Again, grill #2 must be one of the three selected. How many different ways can the three grill displays be selected if customers view the grills in order?

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