Math Problem Statement

The probability of an event is given. Find the odds in favor of the event.

0.4

Solution

The odds in favor of an event are calculated using the probability of the event occurring.

Given the probability of the event P(E)=0.4P(E) = 0.4, the formula for the odds in favor of the event is:

Odds in favor of event=P(E)1P(E)\text{Odds in favor of event} = \frac{P(E)}{1 - P(E)}

Substituting the given probability:

Odds in favor=0.410.4=0.40.6=23\text{Odds in favor} = \frac{0.4}{1 - 0.4} = \frac{0.4}{0.6} = \frac{2}{3}

Therefore, the odds in favor of the event are 23\frac{2}{3}.

Would you like a detailed explanation of how odds are derived from probability?

Here are 5 related questions:

  1. What are the odds against the event occurring?
  2. If the odds in favor of an event are 3:2, what is the probability of the event?
  3. How do you convert odds against an event into probability?
  4. If the probability of an event is 0.75, what are the odds in favor of the event?
  5. How do you calculate the probability of complementary events?

Tip: The sum of probabilities of an event and its complement always equals 1.

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Math Problem Analysis

Mathematical Concepts

Probability
Odds

Formulas

Odds in favor = P(E) / (1 - P(E))

Theorems

Complementary Probability

Suitable Grade Level

Grades 8-10