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Chapter 8: Problem 31

The probability of an event \(E\) not occurring is .6. What are the odds in favor of \(E\) occurring? What are the odds against \(E\) occurring?

Short Answer

Expert verified
The probability of event \(E\) occurring is \(0.4\), while the probability of it not occurring is \(0.6\). Thus, the odds in favor of \(E\) occurring are \(\frac{2}{3}\) or \(2:3\), and the odds against \(E\) occurring are \(\frac{3}{2}\) or \(3:2\).

Step by step solution

01

Find the probability of E occurring

We are given the probability of E not occurring, which we can represent as P(not E) = 0.6. Since the sum of the probabilities of an event occurring and not occurring is always 1, we can find the probability of E occurring by subtracting the given probability from 1: P(E) = 1 - P(not E) = 1 - 0.6 = 0.4
02

Determine the odds in favor of E occurring

Odds in favor of an event occurring are calculated as a ratio of the probability of the event happening to the probability of the event not happening. In this case, we can represent the odds in favor of E occurring as: Odds in favor of E = P(E) / P(not E) Now, we can substitute the probabilities that we calculated in Step 1 to get: Odds in favor of E = \( \frac{0.4}{0.6} = \frac{2}{3} \) So, the odds in favor of E occurring are 2:3.
03

Determine the odds against E occurring

Odds against an event occurring are the inverse of the odds in favor of the event occurring. In other words, we simply switch the values in the ratio that we calculated in Step 2. So, the odds against E occurring can be represented as: Odds against E = P(not E) / P(E) Substitute the probabilities that we calculated in Step 1: Odds against E = \( \frac{0.6}{0.4} = \frac{3}{2} \) So, the odds against E occurring are 3:2.

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