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?

Question

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.