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

Concept:

Event of selecting a particular company = P (E)

Event of choosing a defective product from companies A, B and C be P (A), P (B) and P (C) respectively.

Probability of choosing a defective product, produced by A = P (E) × \(P (\frac{A}{E})\)

Probability of choosing a defective product, produced by B = P (E) × \(P (\frac{B}{E})\)

Probability of choosing a defective product, produced by C = P (E) × \(P (\frac{C}{E})\)

Probability that product chosen is defective, P (D) =  P (E) × \(P (\frac{A}{E})\) +  P (E) × \(P (\frac{B}{E})\) + P (E) × \(P (\frac{C}{E})\)

Calculation:

Given:

Since there are three companies, P (E) = \(\frac{1}{3}\)

Company A products 10% defective products, \(P (\frac{A}{E})\) = \(\frac{10}{100}\)

Company B produces 20% defective products, \(P (\frac{B}{E})\) = \(\frac{20}{100}\)

Company C produces 5% defective products, \(P (\frac{C}{E})\) = \(\frac{5}{100}\)

Probability that product chosen is defective, P (D) = \(\frac{1}{3}\) × [ \(\frac{10}{100}\) + \(\frac{20}{100}\) + \(\frac{5}{100}\) ]

⇒ P (D) = \(\frac{1}{3}\) × \(\frac{35}{100}\) = 0.12