Question

Determine the probability of each event if you randomly select a cube from a bag containing 6 red cubes, 4 yellow cubes, 3 blue cubes, and 1 green cube.

P(red)

Short answer

The probability of the event if you randomly select a red cube from a bag is $\mathit{P}\left(\text{red}\right)\mathbf{=}\frac{\mathbf{3}}{\mathbf{7}}$.

Step-by-step solution

Step 1. Define the concept.

The probability of an event is the ratio of the number of favorable outcomes for the event to the total number of possible outcomes.

Step 2. Define the sample space. 

Sample space is defined as all possible outcomes. Here, bag contains 6 red cubes, 4 yellow cubes, 3 blue cubes, and 1 green cube, therefore,

$\begin{array}{c}\text{Totaloutcomes}=6+4+3+1\\ =14\end{array}$

Step 3. Determine the probability.

To find the probability to select red cubes P(red), divide the number of red cubes by total outcomes.

$$\begin{gathered} \text{probability=}\frac{\text{numberoffavorableoutcomes}}{\text{totalnumberofpossibleoutcomes}} \\ =\frac{6}{14} \\ P\left(\text{red}\right)=\frac{3}{7} \end{gathered}$$

Therefore, $P\left(\text{red}\right)=\frac{3}{7}$.