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From a set of thirteen marbles, six green and seven yellow, we choose one at random.
a. What are the odds in favor of choosing a green marble?
b. What are the odds against choosing a green marble?
a. The odds in favor of choosing a green marble are .
(Simplify your answers.)

Ask by Burns Gonzalez. in the United States
Jan 22,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

a. The odds in favor of choosing a green marble are 6:7.
b. The odds against choosing a green marble are 7:6.

Solution

Let’s analyze the problem step by step.

Given:

  • Total marbles: 13
    • Green marbles: 6
    • Yellow marbles: 7

a. Odds in Favor of Choosing a Green Marble

Odds in favor are calculated as the ratio of the number of favorable outcomes to the number of unfavorable outcomes.
  • Favorable outcomes (green marbles): 6
  • Unfavorable outcomes (yellow marbles): 7
So, the odds in favor of choosing a green marble are:

b. Odds Against Choosing a Green Marble

Odds against are the inverse of odds in favor, meaning they are calculated as the ratio of unfavorable outcomes to favorable outcomes.
  • Unfavorable outcomes (yellow marbles): 7
  • Favorable outcomes (green marbles): 6
Thus, the odds against choosing a green marble are:

Summary of Answers:

  • a. The odds in favor of choosing a green marble are .
  • b. The odds against choosing a green marble are .

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

Beyond the Answer

To determine the odds in favor of choosing a green marble, we first identify the number of green and yellow marbles. There are 6 green marbles and 7 yellow marbles, making a total of 13 marbles. The odds in favor of selecting a green marble can be expressed as the ratio of the number of green marbles to the number of yellow marbles. This gives us .
For the odds against choosing a green marble, we simply reverse the ratio. The odds against are the number of yellow marbles to the number of green marbles, which results in .
So, the answers are:
a. The odds in favor of choosing a green marble are .
b. The odds against choosing a green marble are .

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