A box contains 50 bolts and 150 nuts. On checking the box, it was found that half of the bolts and half of the nuts are rusted. If one item is chosen at random, find the probability that it is rusted

Options

A. `1//4`
B. `1//2`
C. `1//5`
D. `1//15`

Answer

To solve the problem step-by-step, we will follow these steps:

### Step 1: Identify the total number of bolts and nuts
- Total bolts = 50
- Total nuts = 150

### Step 2: Calculate the number of rusted bolts and nuts
- Since half of the bolts are rusted:
\[ \text{Rusted bolts} = \frac{50}{2} = 25 \]
- Since half of the nuts are rusted:
\[ \text{Rusted nuts} = \frac{150}{2} = 75 \]

### Step 3: Calculate the total number of rusted items
- Total rusted items = Rusted bolts + Rusted nuts
\[ \text{Total rusted items} = 25 + 75 = 100 \]

### Step 4: Calculate the total number of items in the box
- Total items = Total bolts + Total nuts
\[ \text{Total items} = 50 + 150 = 200 \]

### Step 5: Calculate the probability of selecting a rusted item
- Probability (P) of selecting a rusted item is given by the formula:
\[ P(\text{rusted}) = \frac{\text{Number of rusted items}}{\text{Total number of items}} = \frac{100}{200} \]
- Simplifying this fraction:
\[ P(\text{rusted}) = \frac{1}{2} \]

### Final Answer:
The probability that a randomly chosen item is rusted is \(\frac{1}{2}\).

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