Question

What are the odds against choosing a green or red marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?
A.5:14
B.5:9
C.9:14
D.9:5
Best answer

Answer 1

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**