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 :
is of metal :

Options

A. `17//25`
B. `25//17`
C. `3//5`
D. `2//25`

Answer

To find the probability that a randomly selected utensil is of metal, we can follow these steps:

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

**Total number of utensils (nt)** = Number of steel utensils + Number of aluminium utensils + Number of glass utensils
\[ nt = 150 + 20 + 80 = 250 \]

### Step 2: Identify the number of metal utensils
Metal utensils include both steel and aluminium. Therefore, we calculate:
- Number of metal utensils = Number of steel utensils + Number of aluminium utensils
\[ \text{Number of metal utensils (nf)} = 150 + 20 = 170 \]

### Step 3: Calculate the probability
The probability (P) of selecting a metal utensil is given by the formula:
\[ P(\text{metal}) = \frac{\text{Number of favourable outcomes (nf)}}{\text{Total number of outcomes (nt)}} \]
Substituting the values we found:
\[ P(\text{metal}) = \frac{170}{250} \]

### Step 4: Simplify the fraction
To simplify \(\frac{170}{250}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 10:
\[ P(\text{metal}) = \frac{170 \div 10}{250 \div 10} = \frac{17}{25} \]

### Final Answer
The probability that the selected utensil is of metal is:
\[ \frac{17}{25} \]

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