To find the odds against choosing a red marble from the bag, we first need to determine the total number of marbles and the number of marbles that are not red.
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Total number of marbles:
- Blue marbles: 2
- Green marbles: 1
- White marbles: 7
- Red marbles: 4
Total = 2 + 1 + 7 + 4 = 14 marbles
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Number of marbles that are not red:
- Total marbles - Red marbles = 14 - 4 = 10 marbles
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Odds against choosing a red marble:
- The odds against an event is the ratio of the number of outcomes against the event to the number of outcomes for the event.
- Here, the outcomes against (not choosing a red marble) = 10
- The outcomes for (choosing a red marble) = 4
Therefore, the odds against choosing a red marble are:
\[ \text{Odds against red} = \frac{\text{Number of non-red marbles}}{\text{Number of red marbles}} = \frac{10}{4} = \frac{5}{2} \]
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Expressing odds in a ratio format: The odds against choosing a red marble can also be expressed as 5:2.
However, looking at the provided options, it seems none exactly match this. To find the best answer:
When we normalize from the fractions we found:
- The odds against (10 non-red : 4 red) = 10:4 simplifies to 5:2.
Among the choices provided we actually note: A. 4:10 B. 10:4 (which is equivalent to 5:2) C. 13:1 D. 14:4
The best option from those available in the context of your question, considering that normalized form we have is:
B. 10:4