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?

A. 4:10
B. 10:4
C. 13:1
D. 14:4
Best answer

1 answer

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.

  1. Total number of marbles:

    • Blue marbles: 2
    • Green marbles: 1
    • White marbles: 7
    • Red marbles: 4

    Total = 2 + 1 + 7 + 4 = 14 marbles

  2. Number of marbles that are not red:

    • Total marbles - Red marbles = 14 - 4 = 10 marbles
  3. 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:

    \[ \text{Odds against red} = \frac{\text{Number of non-red marbles}}{\text{Number of red marbles}} = \frac{10}{4} = \frac{5}{2} \]

  4. 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