Question

What are the odds against choosing a blue or green marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?
A. 5:14
B. 3:14
C. 3:11
D. 11:3
Best answer

Answer 1

To solve the problem, we first need to determine the total number of marbles in the bag and the number of favorable outcomes for choosing a blue or green marble.

1. **Count the marbles**:
- Blue marbles: 2
- Green marbles: 1
- White marbles: 7
- Red marbles: 4

Total number of marbles = 2 (blue) + 1 (green) + 7 (white) + 4 (red) = 14 marbles.

2. **Count the favorable outcomes**:
- Favorable outcomes (blue or green) = 2 (blue) + 1 (green) = 3 marbles.

3. **Count the unfavorable outcomes**:
- Non-blue and non-green marbles (white and red) = 7 (white) + 4 (red) = 11 marbles.

4. **Calculate the odds against choosing a blue or green marble**:
- The odds against an event is the ratio of unfavorable outcomes to favorable outcomes.
- Unfavorable outcomes = 11
- Favorable outcomes = 3

Therefore, the odds against choosing a blue or green marble is \( 11:3 \).

Thus, the answer is **D. 11:3**.