# Solved-Party Affiliation The following data represent political party by age from a random sample of regist

#### ByDr. Raju Chaudhari

Oct 6, 2020

Party Affiliation The following data represent political party by age from a random sample of registered Iowa Voters.

. 17-29 30-44 45=64 65+ Total
Republican 224 340 1075 561 2200
Democrat 184 384 773 459 1800
Total 408 724 1848 1020 4000

(c) Are the events "17-29" and "45-64" mutually exclusive? Justify your answer.
(d) Are the events "Republican" and "45-64" mutually exclusive? Justify your answer.

#### Solution

(a)

 \begin{aligned} P(\text{Republican})&=\frac{2200}{4000}\\ &= 0.55. \end{aligned}

 \begin{aligned} P(\text{30-44 age})&=\frac{724}{4000}\\ &= 0.181. \end{aligned}

 \begin{aligned} P(\text{Republican} \cap \text{30-44 age})&=\frac{340}{4000}\\ &= 0.085. \end{aligned}

 \begin{aligned} P(\text{Republican})*P(\text{30-44 age})&=0.55 \times 0.181\\ &=0.09955\\ &\neq P(\text{Republican} \cap \text{30-44 age}) \end{aligned}

The events "Republican" and "30-44" are not independent.

(b)

 \begin{aligned} P(\text{Democrat})&=\frac{1800}{4000}\\ &= 0.45. \end{aligned}

 \begin{aligned} P(\text{65+ age})&=\frac{1020}{4000}\\ &= 0.255. \end{aligned}

 \begin{aligned} P(\text{Democrat} \cap \text{65+ age})&=\frac{459}{4000}\\ &= 0.11475. \end{aligned}

 \begin{aligned} P(\text{Democrat})*P(\text{65+ age})&=0.45 \times 0.255\\ &=0.11475\\ &=P(\text{Democrat} \cap \text{65+ age}) \end{aligned}

The events "Democrat" and "65+" are independent.

(c) $\text{(17-29) age} \cap \text{(45-64) age}=\phi$, thus the events "17-29" and "45-64" are mutually exclusive.

(d) $\text{(Republican)} \cap \text{(45-64) age}\neq \phi$, the events "Republican" and "45-64" are not mutually exclusive.