7. Aggregates for the construction of a reinforced concrete building are supplie

Question

7. Aggregates for the construction of a reinforced concrete building are supplied by two companies, Company A and Company B. Orders are for Company A to deliver 300 truck loads a day and 700 truck loads a day from Company B. From prior experience, it is expected that 3% of the material from Company A will be substandard, whereas 6% of the material from Company B are substandard.

(A) Calculate the probability that a load of aggregates is not substandard.

(B) When you randomly choose a load of aggregates, calculate the probability that it is from the company B and is not substandard.

Explanation / Answer

P(company A) = 300/1000 = 0.3

P(company B) = 700/1000 = 0.7

P(material is substandard | company A) = 0.03

P(material is not substandard | company A) = 0.97

P(material is substandard | company B) = 0.06

P(material is not substandard | company B) = 0.94

a) P(material is not substandard) = P(material is not substandard | company A) * P(company A) + P(material is not substandard | company B) * P(company B)

                                                     = 0.97 * 0.3 + 0.94 * 0.7

                                                     = 0.949

b) P(Company B and is not substandard) = P(material is not substandard | company B) * P(company B)

                                                   = 0.94 * 0.7

                                                   = 0.658

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