The phrase "Dogs of the Dow" refers to the stocks listed in the Dow with the highest dividend yield. This table shows the top ten stocks of the "Dogs of the Dow" list. If you selected four of these stocks at random, what is the probability that your selection included the company with the highest yield and excluded the company with the lowest yield $$\begin{array} { | c | c | c | }
\hline \text { Symbol } & \text { Company } & \text { Yield } \
\hline \text { SBC } & \text { SBC Communications } & 5.46 \% \
\hline \text { GM } & \text { General Motors } & 5.46 \% \
\hline \text { MRK } & \text { Merck } & 5.42 \% \
\hline \text { MO } & \text { Altria } & 4.62 \% \
\hline \text { VZ } & \text { Verizon } & 4.32 \% \
\hline \text { JPM } & \text { JP Morgan Chase } & 3.78 \% \
\hline \text { C } & \text { Citigroup } & 3.64 \% \
\hline \text { PFE } & \text { Pfizer } & 3.12 \% \
\hline \text { DD } & \text { DuPont } & 2.96 \% \
\hline \text { GE } & \text { General Electric } & 2.46 \% \
\hline
\end{array}$$
A) $\frac { 1 } { 15 }$
B) $\frac { 1 } { 9 }$
C) $\frac { 4 } { 15 }$
D) $\frac { 9 } { 10 }$
E) $\frac { 2 } { 9 }$

Question

The phrase "Dogs of the Dow" refers to the stocks listed in the Dow with the highest dividend yield. This table shows the top ten stocks of the "Dogs of the Dow" list. If you selected four of these stocks at random, what is the probability that your selection included the company with the highest yield and excluded the company with the lowest yield  $$\begin{array} { | c | c | c | } 
\hline \text { Symbol } & \text { Company } & \text { Yield } \
\hline \text { SBC } & \text { SBC Communications } & 5.46 \% \
\hline \text { GM } & \text { General Motors } & 5.46 \% \
\hline \text { MRK } & \text { Merck } & 5.42 \% \
\hline \text { MO } & \text { Altria } & 4.62 \% \
\hline \text { VZ } & \text { Verizon } & 4.32 \% \
\hline \text { JPM } & \text { JP Morgan Chase } & 3.78 \% \
\hline \text { C } & \text { Citigroup } & 3.64 \% \
\hline \text { PFE } & \text { Pfizer } & 3.12 \% \
\hline \text { DD } & \text { DuPont } & 2.96 \% \
\hline \text { GE } & \text { General Electric } & 2.46 \% \
\hline
\end{array}$$  
A) $\frac { 1 } { 15 }$
B) $\frac { 1 } { 9 }$
C) $\frac { 4 } { 15 }$
D) $\frac { 9 } { 10 }$
E) $\frac { 2 } { 9 }$

Quizplus · Accepted Answer

To find the probability of selecting the company with the highest yield and excluding the company with the lowest yield, we first identify these companies. The highest yield is 5.46% (SBC or GM), and the lowest yield is 2.46% (GE). We must include one of the highest yield companies (2 options) and exclude the lowest yield company, selecting 3 more from the remaining 8 (not including the highest yield company already chosen and the lowest yield company). The number of ways to choose these 3 companies is $\binom{8}{3}$. The total number of ways to choose any 4 companies from the 9 (excluding GE) is $\binom{9}{4}$. The probability is then $\frac{2 \times \binom{8}{3}}{\binom{9}{4}} = \frac{2 \times 56}{126} = \frac{112}{126} = \frac{4}{15}$.

The Phrase "Dogs of the Dow" Refers to the Stocks