Question

A bag contains $40$ marbles: $12$ red, $12$ blue, and $16$ yellow.

What is the probability that a blue is randomly selected?

• A. $0.30$
• B. $0.33$
• C. $0.40$
• D. $0.60$

Answer 1

The correct option is A

$0.30$

To find the probability for the blue is select:

The total number of marbles are $40$.

The probability for that the blue is randomly selected by using the basic formula of the probability $\text{P}\left(\text{E}\right)=\frac{\text{Number of trails}}{\text{Total number of trails}}$ is below:

$\begin{array}{rcl}\text{P}\left(E\right)& =& \frac{{}^{12}C_1}{{}^{40}C_1}\\ & \Rightarrow & \text{P}\left(E\right)=\frac{12}{40}\left[\because {}^{n}C_1=n\right]\\ \therefore \text{P}\left(E\right)& =& 0.30\end{array}$

Explanation for correct option: Option $\left(\text{A}\right)$

The option $\left(\text{A}\right)$ is equal to the obtained answer.

Therefore the option $\left(\text{A}\right)$ is correct.

Explanation for incorrect options:

Option $\left(\text{B}\right)$

The option $\left(\text{B}\right)$ is not equivalent to the obtained answer.

Therefore, the option $\left(\text{B}\right)$ is incorrect.

Option $\left(\text{C}\right)$

The option $\left(\text{C}\right)$ is not equivalent to the obtained answer.

Therefore, the option $\left(\text{C}\right)$ is incorrect.

Option $\left(\text{D}\right)$

The option $\left(\text{D}\right)$ is not equivalent to the obtained answer.

Therefore, the option $\left(\text{D}\right)$ is incorrect.

Hence, option $\left(\text{A}\right)$ is the correct answer.