Solution Found!
Choosing portable grill displays. University of Maryland
Chapter 3, Problem 23E(choose chapter or problem)
Choosing portable grill displays. University of Maryland marketing professor R. W. Hamilton studied how people attempt to influence the choices of others by offering undesirable alternatives (Journal of Consumer Research, Mar. 2003). Such a phenomenon typically occurs when family members propose a vacation spot, friends recommend a restaurant for dinner, and realtors show the buyer potential homes. In one phase of the study, the researcher had each of 124 college students select showroom displays for portable grills. Five different displays (representing five differentsized grills) were available, but only three displays would be selected. The students were instructed to select the displays to maximize purchases of Grill #2 (a smaller-sized grill).
a. In how many possible ways can the three grill displays be selected from the five displays? List the possibilities.
b. The table shows the grill display combinations and the number of each selected by the 124 students. Use this information to assign reasonable probabilities to the different display combinations.
c. Find the probability that a student who participated in the study selected a display combination involving Grill #1.
\(\begin{array}{cc}
\hline \text { Grill Display Combination } & \text { Number of Students } \\
\hline 1-2-3 & 35 \\
1-2-4 & 8 \\
1-2-5 & 42 \\
2-3-4 & 4 \\
2-3-5 & 1 \\
2-4-5 & 34 \\
\hline
\end{array}\)
Source: 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, No. 4. Mar. 2003 (Table 1).
Questions & Answers
QUESTION:
Choosing portable grill displays. University of Maryland marketing professor R. W. Hamilton studied how people attempt to influence the choices of others by offering undesirable alternatives (Journal of Consumer Research, Mar. 2003). Such a phenomenon typically occurs when family members propose a vacation spot, friends recommend a restaurant for dinner, and realtors show the buyer potential homes. In one phase of the study, the researcher had each of 124 college students select showroom displays for portable grills. Five different displays (representing five differentsized grills) were available, but only three displays would be selected. The students were instructed to select the displays to maximize purchases of Grill #2 (a smaller-sized grill).
a. In how many possible ways can the three grill displays be selected from the five displays? List the possibilities.
b. The table shows the grill display combinations and the number of each selected by the 124 students. Use this information to assign reasonable probabilities to the different display combinations.
c. Find the probability that a student who participated in the study selected a display combination involving Grill #1.
\(\begin{array}{cc}
\hline \text { Grill Display Combination } & \text { Number of Students } \\
\hline 1-2-3 & 35 \\
1-2-4 & 8 \\
1-2-5 & 42 \\
2-3-4 & 4 \\
2-3-5 & 1 \\
2-4-5 & 34 \\
\hline
\end{array}\)
Source: 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, No. 4. Mar. 2003 (Table 1).
ANSWER:Step 1 of 3
Given 5 different displays were available but 3 displays would selected.
Then the students were instructed to select the displays to maximize purchases of Grill #2.
Our goal is:
a). We need to find how many possible ways can the three grill displays be selected from
the 5 displays and we list the possibilities.
b). Use the information to assign reasonable probabilities to the different display
Combinations.
c). We need to find to probability that a student who participated in the study
selected a display combination involving Grill #1.
a).
Now we have to find how many possible ways can the three grill displays be selected from the 5 displays and we list the possibilities.
From the given information we know that the students are instructed purchases of Grill #2 must always be one of the 3 grill displayed.
From the 4 remaining option we can choose 2 other grills.
Hence it represents a combination of 4 items taken 2 at a time.
Now we are using the Combinations Rule.
Then the number of possible grill is
\(\begin{array}{l}
\left(\begin{array}{l}
4 \\
2
\end{array}\right)=\frac{4 !}{2 !(4-2) !} \\
\left(\begin{array}{l}
4) \\
2
\end{array}=\frac{4 !}{2 !(2) !}\right. \\
=\frac{4 \times 3 \times 2 \times 1}{2 \times 1(2 \times 1)} \\
=\frac{24}{4} \\
=6
\end{array}\)
Therefore 6 possible display combinations are there.
Now we have to list the 6 possible display combinations.
1-2-3, 1-2-4, 1-2-5, 2-3-4, 2-3-5, 2-4-5.