Answer
a. $0.256$
b. $0.731$
c. $0.929$
“Republican” and “term expires in 2015” are not independent
Work Step by Step
Total number = 78
a. P(Democrat and term expires in 2015)
$p=20/78=0.256$
b. P(Republican or term expires in 2013)
P(Republican)=$36/78=0.462$
P(term expires in 2013)=$29/78=0.372$
P(Republican and term expires in 2013)=$8/78=0.103$
P(Republican or term expires in 2013)=$0.462+0.372-0.103=0.731$
c. P(Republican given term expires in 2017)
P(term expires in 2017)=$14/78$
P(Republican and term expires in 2017)=$13/78$
P(Republican given term expires in 2017)=$13/14=0.929$
P(Republican)=$36/78$
P(term expires in 2015)=$35/78$
P(Republican and term expires in 2015)=$15/78$
Since P(Republican and term expires in 2015)$\ne$P(Republican)$\times$P(term expires in 2015)
“Republican” and “term expires in 2015” are not independent
Alternatively we can prove that P(Republican given term expires in 2015)$\ne$P(Republican)
