In a toys making factory, machine A, B and C manufacture respectively `25%,35%"and" 40%` of the total toys. Of their output `5%,4% "and " 2%` respectively are defective toys . A toy is drawn at random from the product. What is the probability that the toy drawn is defective?

Options

A. 0.225
B. 0.0345
C. 0.235
D. none of these

Answer

To solve the problem step by step, we will calculate the total number of defective toys produced by each machine and then find the overall probability of drawing a defective toy.

### Step 1: Determine the total number of toys produced by each machine.
Assuming the total number of toys produced is 100 (for simplicity), we can calculate the number of toys produced by each machine:

- Machine A produces 25% of the total toys:
\[ \text{Toys produced by A} = 25\% \times 100 = 25 \text{ toys} \]

- Machine B produces 35% of the total toys:
\[ \text{Toys produced by B} = 35\% \times 100 = 35 \text{ toys} \]

- Machine C produces 40% of the total toys:
\[ \text{Toys produced by C} = 40\% \times 100 = 40 \text{ toys} \]

### Step 2: Calculate the number of defective toys from each machine.
Next, we will calculate the number of defective toys produced by each machine based on the given percentages of defective toys:

- Machine A has 5% defective toys:
\[ \text{Defective toys from A} = 5\% \times 25 = 0.05 \times 25 = 1.25 \text{ toys} \]

- Machine B has 4% defective toys:
\[ \text{Defective toys from B} = 4\% \times 35 = 0.04 \times 35 = 1.4 \text{ toys} \]

- Machine C has 2% defective toys:
\[ \text{Defective toys from C} = 2\% \times 40 = 0.02 \times 40 = 0.8 \text{ toys} \]

### Step 3: Calculate the total number of defective toys.
Now, we will sum the defective toys from all machines to find the total number of defective toys:
\[ \text{Total defective toys} = \text{Defective from A} + \text{Defective from B} + \text{Defective from C} \]
\[ \text{Total defective toys} = 1.25 + 1.4 + 0.8 = 3.45 \text{ toys} \]

### Step 4: Calculate the probability of drawing a defective toy.
The probability of drawing a defective toy is given by the ratio of the total number of defective toys to the total number of toys produced:
\[ P(\text{Defective}) = \frac{\text{Total defective toys}}{\text{Total toys}} = \frac{3.45}{100} = 0.0345 \]

### Final Answer:
Thus, the probability that the toy drawn is defective is:
\[ P(\text{Defective}) = 0.0345 \]

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