12. Company A produces $$ 10 \% $$ defective products, Company B produces $$ 20 \% $$ defective products and C produces $$ 5 \% $$ defective products. If choosing a company is an equally likely event, then what is the probability that the product chosen is defective?

Question

UpStudy AI · Accepted Answer

To determine the probability that a randomly chosen product is defective, we can use the **Law of Total Probability**. Here's a step-by-step breakdown:

1. **Identify the Probabilities:**
   - **Probability of choosing each company:**
     - Company A: $$ \frac{1}{3} $$
     - Company B: $$ \frac{1}{3} $$
     - Company C: $$ \frac{1}{3} $$
   - **Probability of a defective product from each company:**
     - Company A: $$ 10\% = 0.10 $$
     - Company B: $$ 20\% = 0.20 $$
     - Company C: $$ 5\% = 0.05 $$

2. **Apply the Law of Total Probability:**
   $$
   P(\text{Defective}) = P(A) \times P(\text{Defective} | A) + P(B) \times P(\text{Defective} | B) + P(C) \times P(\text{Defective} | C)
   $$
   Plugging in the values:
   $$
   P(\text{Defective}) = \left(\frac{1}{3} \times 0.10\right) + \left(\frac{1}{3} \times 0.20\right) + \left(\frac{1}{3} \times 0.05\right)
   $$
   $$
   P(\text{Defective}) = \frac{0.10 + 0.20 + 0.05}{3} = \frac{0.35}{3} \approx 0.1167
   $$

3. **Convert to Percentage:**
   $$
   0.1167 \times 100 \approx 11.67\%
   $$

**Final Answer:** The probability of selecting a defective product is approximately 11.67 %.
The probability of selecting a defective product is approximately 11.67%.

Company A produces defective products, Company B produces
defective products and C produces defective products. If choosing a
company is an equally likely event, then what is the probability that the
product chosen is defective?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Probability Questions

Company A produces defective products, Company B produces defective products and C produces defective products. If choosing a company is an equally likely event, then what is the probability that the product chosen is defective?