What are the odds against choosing a red marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?
Question
What are the odds against choosing a red marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?
Solution
To determine the odds against choosing a red marble from the bag, follow these steps:
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Count the total number of marbles:
- Blue marbles: 2
- Green marbles: 1
- White marbles: 7
- Red marbles: 4
Total marbles = 2 + 1 + 7 + 4 = 14
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Count the number of red marbles:
- Red marbles = 4
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Calculate the number of non-red marbles:
- Non-red marbles = Total marbles - Red marbles
- Non-red marbles = 14 - 4 = 10
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Determine the odds against choosing a red marble:
- Odds against = Number of non-red marbles : Number of red marbles
- Odds against = 10 : 4
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Simplify the ratio:
- Simplified ratio = 10 ÷ 2 : 4 ÷ 2
- Simplified ratio = 5 : 2
Therefore, the odds against choosing a red marble from the bag are 5:2.
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