Problem

Points: 0 of 1 If $P(E)=0.11$, find the odds against $E$. What are the odds against $E$ ? Select the correct choice below and fill in the answer box(es) to complete your answer. A. The odds are $\square$ to $\square$. (Type integers or decimals.) B. The odds are (Type an integer or a decimal.)

Solution

Step 1 :Given that the probability of event E, denoted as \(P(E)\), is 0.11.

Step 2 :The probability that event E will not occur, denoted as \(P(\neg E)\), is calculated as 1 - \(P(E)\), which equals 1 - 0.11 = 0.89.

Step 3 :The odds against E is the ratio of the probability that the event will not occur to the probability that the event will occur, which is \(\frac{P(\neg E)}{P(E)}\).

Step 4 :Substituting the given values, we get \(\frac{0.89}{0.11}\) = 8.09.

Step 5 :Therefore, the odds against E are \(\boxed{8.09}\) to \(\boxed{1}\).

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