Among the workers in a factory only 30% receive bonus and among those receiving bonus only 20% are skilled. The probability that a randomly selected worker is skilled and is receiving bonus, is

Options

A. `0.03`
B. `0.02`
C. `0.06`
D. `0.015`

Answer

To find the probability that a randomly selected worker is both skilled and receiving a bonus, we can follow these steps:

### Step 1: Determine the probability of receiving a bonus
According to the problem, only 30% of the workers receive a bonus. This can be expressed as a fraction:
\[ P(\text{Bonus}) = 0.30 = \frac{3}{10} \]

### Step 2: Determine the probability of being skilled among those who receive a bonus
Among the workers who receive a bonus, only 20% are skilled. This can also be expressed as a fraction:
\[ P(\text{Skilled} | \text{Bonus}) = 0.20 = \frac{2}{10} \]

### Step 3: Calculate the probability of being skilled and receiving a bonus
To find the probability that a worker is both skilled and receiving a bonus, we use the formula for conditional probability:
\[ P(\text{Skilled and Bonus}) = P(\text{Bonus}) \times P(\text{Skilled} | \text{Bonus}) \]
Substituting the values we found:
\[ P(\text{Skilled and Bonus}) = \frac{3}{10} \times \frac{2}{10} = \frac{6}{100} \]

### Step 4: Simplify the probability
The fraction \(\frac{6}{100}\) can be simplified to:
\[ P(\text{Skilled and Bonus}) = 0.06 \]

### Final Answer
The probability that a randomly selected worker is skilled and receiving a bonus is:
\[ \boxed{0.06} \]