A bag contains 30 red, 40 blue, and
50 white buttons. You pick one button
at random. Find the probability that it
is blue or not red.

Ask by Mejia Campbell. in South Africa

Jan 22,2025

Question

A bag contains 30 red, 40 blue, and 50 white buttons. You pick one button at random. Find the probability that it is blue or not red. $$ P \text { (blue or not red) }=\text { [?] } $$

UpStudy AI · Accepted Answer

To determine the probability of selecting a button that is **blue or not red**, let's break down the problem step by step.

### **Given:**
- **Red buttons:** 30
- **Blue buttons:** 40
- **White buttons:** 50
- **Total buttons:** $$ 30 + 40 + 50 = 120 $$

### **Understanding "Blue or Not Red":**
- **"Not Red"** includes both blue and white buttons.
- Therefore, "blue or not red" essentially covers all buttons **except** the red ones.

### **Calculating the Probability:**
1. **Count of Buttons That Are Not Red:**
   $$
   \text{Not Red} = \text{Blue} + \text{White} = 40 + 50 = 90
   $$
   
2. **Total Number of Buttons:**
   $$
   \text{Total} = 120
   $$
   
3. **Probability:**
   $$
   P(\text{blue or not red}) = \frac{\text{Number of Not Red Buttons}}{\text{Total Number of Buttons}} = \frac{90}{120} = \frac{3}{4}
   $$

### **Final Answer:**
$$
P \text{ (blue or not red) } = \frac{3}{4}
$$
The probability of picking a blue or not red button is $$ \frac{3}{4} $$.

A bag contains 30 red, 40 blue, and
50 white buttons. You pick one button
at random. Find the probability that it
is blue or not red.

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