To find the odds against choosing a green or red marble, we first need to determine the total number of marbles and the number of favorable outcomes for choosing a green or red marble.
Step 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.
Step 2: Find the number of favorable outcomes for choosing a green or red marble.
- Favorable outcomes (green + red) = 1 (green) + 4 (red) = 5 marbles.
Step 3: Calculate the number of outcomes that are not favorable (not choosing a green or red marble).
- Non-favorable outcomes = Total marbles - Favorable marbles = 14 - 5 = 9 non-favorable marbles (which are the blue and white marbles).
Step 4: Calculate the odds against choosing a green or red marble. Odds against an event are given by the ratio of the number of non-favorable outcomes to the number of favorable outcomes.
Odds against choosing a green or red marble = Number of non-favorable outcomes : Number of favorable outcomes = 9 : 5.
So the correct answer is:
D. 9:5