Question

What are the odds against choosing a blue marble from a bag that contains two blue marbles, one green marble, seven white marbles, and four red marbles?

• A. $12:2$
• B. $2:14$
• C. $14:2$
• D. $10:2$

Answer 1

The correct option is A

$12:2$

Explanation for the correct answer:

The bag contains two blue marbles, one green marble, 7 white marbles, and 4 red marbles.

Add $2,1,7,4$ to obtain the total number of marbles.

$2+1+7+4=14$

The odds in against is $\frac{12}{14}$.

Substitute $\frac{12}{14}$ for the probability of against odds and $\frac{2}{14}$ for the probability of success:

$$\begin{gathered} \frac{q}{p}=\frac{\text{Probability of against}}{\text{Probabilty of success}} \\ \Rightarrow \frac{q}{p}=\frac{{\displaystyle \frac{12}{14}}}{{\displaystyle \frac{2}{14}}} \\ \Rightarrow \frac{q}{p}=\frac{12}{2} \\ \therefore p:q=12:2 \end{gathered}$$

Hence, option (A) is correct.