Problem

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 $=\square$

Answer

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Answer

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

Steps

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 \(\boxed{0.33:1}\)

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