Certainly! Let's go through the problem step-by-step to find the probability of picking a button that is not blue from the bag.
1. Determine the Total Number of Buttons:
- The bag contains 30 red buttons, 40 blue buttons, and 50 white buttons.
- To find the total number of buttons in the bag, we add these amounts together:
[tex]\[
\text{Total buttons} = 30 + 40 + 50 = 120
\][/tex]
2. Find the Number of Blue Buttons:
- According to the problem, there are 40 blue buttons in the bag.
3. Calculate the Probability of Picking a Blue Button:
- The probability of picking a blue button is the ratio of the number of blue buttons to the total number of buttons:
[tex]\[
P(\text{blue}) = \frac{\text{Number of blue buttons}}{\text{Total number of buttons}} = \frac{40}{120} = \frac{1}{3} \approx 0.3333
\][/tex]
4. Calculate the Probability of Not Picking a Blue Button:
- The probability of not picking a blue button is the complement of the probability of picking a blue button. This means it is one minus the probability of picking a blue button:
[tex]\[
P(\text{not blue}) = 1 - P(\text{blue}) = 1 - \frac{1}{3} = \frac{2}{3} \approx 0.6667
\][/tex]
Thus, the probability of picking a button that is not blue from the bag is:
[tex]\[
P(\text{not blue}) = \frac{2}{3} \approx 0.6667
\][/tex]
