Q3. - Algebra 1

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(not red)

Step-by-Step Solution

Answer

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

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, 

$$\begin{gathered} \text{Total outcomes }=6+4+3+1 \\ =14 \end{gathered}$$ 

Step 3. Determine the probability.

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

$$\begin{gathered} \text{probability =}\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} \\ =\frac{6}{14} \\ P\left(\text{red}\right)=\frac{3}{7} \end{gathered}$$ 

 

Now subtract the red cube probability from 1 to find the probability of P(not red),

$$\begin{gathered} \text{P}\left(\text{not red}\right)=1-\frac{3}{7} \\ =\frac{4}{7} \end{gathered}$$            

 

Therefore, $P\left(\text{not red}\right)=\frac{4}{7}$.