Answer
a.
odds in favor =$\frac{1}{5}$
odds against =$\frac{5}{1}$
b.
odds in favor =$\frac{1}{1}$
odds against =$\frac{1}{1}$
c.
odds in favor =$\frac{1}{3}$
odds against =$\frac{3}{1}$
d.
odds in favor =$\frac{1}{1}$
odds against =$\frac{1}{1}$
e.
odds in favor =$\frac{1}{12}$
odds against =$\frac{12}{1}$
f.
odds in favor =$\frac{1}{3}$
odds against =$\frac{3}{1}$
g.
odds in favor =$\frac{1}{1}$
odds against =$\frac{1}{1}$
Work Step by Step
a. Rolling a die and getting a 2, $p_{1}=1/6, p_{2}=1-p_{1}=5/6$
odds in favor =$\frac{1/6}{1-1/6}=\frac{1}{5}$
odds against =$\frac{5/6}{1-1/6}=\frac{5}{1}$
b. Rolling a die and getting an even number, $p_{1}=3/6=1/2=p_{2}$
odds in favor =$\frac{1/2}{1-1/2}=\frac{1}{1}$
odds against =$\frac{1/2}{1-1/2}=\frac{1}{1}$
c. Drawing a card from a deck and getting a spade, $p_{1}=13/52=1/4, p_{2}=3/4$
odds in favor =$\frac{1/4}{1-1/4}=\frac{1}{3}$
odds against =$\frac{3/4}{1-3/4}=\frac{3}{1}$
d. Drawing a card and getting a red card, $p_{1}=26/52=1/2= p_{2}$
odds in favor =$\frac{1/2}{1-1/2}=\frac{1}{1}$
odds against =$\frac{1/2}{1-1/2}=\frac{1}{1}$
e. Drawing a card and getting a queen, $p_{1}=4/52=1/13, p_{2}=12/13$
odds in favor =$\frac{1/13}{1-1/13}=\frac{1}{12}$
odds against =$\frac{12/13}{1-12/13}=\frac{12}{1}$
f. Tossing two coins and getting two tails, $p_{1}=1/4, p_{2}=3/4$
odds in favor =$\frac{1/4}{1-1/4}=\frac{1}{3}$
odds against =$\frac{3/4}{1-3/4}=\frac{3}{1}$
g. Tossing two coins and getting exactly one tail, $p_{1}=1/2, p_{2}=1/2$
odds in favor =$\frac{1/2}{1-1/2}=\frac{1}{1}$
odds against =$\frac{1/2}{1-1/2}=\frac{1}{1}$