Math Problem Statement

If o(E) = 4:3, find p(E). (Enter your answer as a fraction.)

Solution

The image shows a problem involving odds and probability. It asks to find p(E)p(E) (the probability of event EE) given that the odds of event EE are 4:3.

Here's how we can solve this:

  1. Understanding Odds: The odds o(E)=4:3o(E) = 4:3 means that the ratio of favorable outcomes to unfavorable outcomes is 4 to 3.

  2. Convert Odds to Probability: The probability p(E)p(E) is the ratio of favorable outcomes to the total outcomes (favorable + unfavorable).

    p(E)=favorable outcomesfavorable outcomes+unfavorable outcomes=44+3=47p(E) = \frac{\text{favorable outcomes}}{\text{favorable outcomes} + \text{unfavorable outcomes}} = \frac{4}{4+3} = \frac{4}{7}

Thus, the probability p(E)=47p(E) = \frac{4}{7}.

Would you like more details or have any questions?

Here are 5 follow-up questions to expand on this topic:

  1. What is the difference between probability and odds?
  2. How do you convert odds to probability in general?
  3. What is the probability of the complement of event EE?
  4. How would the probability change if the odds were given as 3:4 instead of 4:3?
  5. Can you express the odds in terms of probability?

Tip: When odds are given, always remember to sum the favorable and unfavorable outcomes to find the total possible outcomes for converting to probability.

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Math Problem Analysis

Mathematical Concepts

Probability
Odds

Formulas

p(E) = \frac{\text{favorable outcomes}}{\text{favorable outcomes} + \text{unfavorable outcomes}}

Theorems

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Suitable Grade Level

Grades 6-8