Given the following probabilities for an event $E$, find the odds for and against $E$. (A) $\frac{1}{9}$ (B) $\frac{3}{4}$ (C) 0.18 (D) 0.59 For all answers, type the odds as a fraction. Simplify your answers. (A) Odds for $=\frac{1}{8}$ Odds against $=\frac{8}{1}$ (B) Odds for $=\square$ Odds against $=\square$

Step 1 ：Given the probability for an event E is \(\frac{3}{4}\)

Step 2 ：Calculate the probability against the event E as \(1 - \frac{3}{4} = \frac{1}{4}\)

Step 3 ：The odds for an event is the ratio of the probability it will happen to the probability that it will not. So, the odds for the event E is \(\frac{3}{4} : \frac{1}{4} = 3:1\)

Step 4 ：The odds against an event is the ratio of the probability that it will not happen to the probability that it will. So, the odds against the event E is \(\frac{1}{4} : \frac{3}{4} = 0.33:1\)

Step 5 ：Final Answer: The odds for the event E is \(\boxed{3:1}\) and the odds against the event E is \(\boxed{0.33:1}\)