There are 150 steel utensils , 20 allumiunm utensils and 80 glass untensils in a kitchen . A untensil is chose at random . Find the probabilityn that the selected utensil is :
not of steel :

Options

A. `3//5`
B. `2//5`
C. `5//3`
D. `5//2`

Answer

To find the probability that a randomly selected utensil is not made of steel, we can follow these steps:

### Step 1: Identify the total number of utensils
We have:
- Steel utensils = 150
- Aluminum utensils = 20
- Glass utensils = 80

**Total utensils** = Steel + Aluminum + Glass
Total = 150 + 20 + 80 = 250

### Step 2: Identify the number of favorable outcomes
The favorable outcomes for the event "not of steel" include both aluminum and glass utensils. Thus, we need to add the number of aluminum and glass utensils:
- Aluminum utensils = 20
- Glass utensils = 80

**Favorable outcomes** = Aluminum + Glass
Favorable = 20 + 80 = 100

### Step 3: Calculate the probability
The probability (P) of selecting a utensil that is not of steel is given by the formula:

\[ P(\text{not steel}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Substituting the values we found:

\[ P(\text{not steel}) = \frac{100}{250} \]

### Step 4: Simplify the fraction
Now we simplify the fraction:

\[ P(\text{not steel}) = \frac{100 \div 50}{250 \div 50} = \frac{2}{5} \]

### Final Answer
The probability that the selected utensil is not of steel is \( \frac{2}{5} \).

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