Math Problem Statement

Two events A and B have probabilities: P left parenthesis A right parenthesis equals 0.36 comma space P left parenthesis B right parenthesis equals space 0.45 comma space P left parenthesis A intersection B right parenthesis space equals space 0.06. What are the odds in favor of event A?

Solution

To find the odds in favor of event AA, we use the following formula:

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

Given:

  • P(A)=0.36P(A) = 0.36

Now, let's calculate the odds:

Odds in favor of A=0.3610.36=0.360.64\text{Odds in favor of } A = \frac{0.36}{1 - 0.36} = \frac{0.36}{0.64}

Simplifying the fraction:

0.360.64=0.5625\frac{0.36}{0.64} = 0.5625

Therefore, the odds in favor of event AA are 0.56250.5625 or 916\frac{9}{16} when expressed as a ratio. This can be interpreted as the odds being 9 to 16 in favor of event AA.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What are the odds against event AA?
  2. How do you calculate the probability of event ABA \cup B (union of AA and BB)?
  3. What is the probability that neither AA nor BB happens?
  4. How are the odds in favor of an event different from the event's probability?
  5. If the events AA and BB are independent, what does P(AB)P(A \cap B) become?

Tip: Odds represent the ratio of favorable to unfavorable outcomes, while probability focuses on favorable outcomes relative to the total possible outcomes.

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Math Problem Analysis

Mathematical Concepts

Probability
Odds

Formulas

Odds in favor of A = P(A) / (1 - P(A))

Theorems

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Suitable Grade Level

Grades 9-11