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 700 truck loads a day and 300 truck loads a day from Company B. From prior experience it is expected that 5% of the material from Company A will be substandard and 3% of the material from Company B will be substandard. Part 1 What is the probability of substandard aggregates

From prior experience, it is expected that 5% of the material from Company A will be substandard and 3% of the material from Company B will be substandard.

Let the probability that orders are for Company A to deliver = P(A) = [tex]\frac{700}{1000}[/tex]

The probability that orders are for Company B to deliver = P(B) = [tex]\frac{300}{1000}[/tex]

Let event S = material which is substandard

So, the probability that the material from Company A will be substandard = P(S/A) = 0.05

the probability that the material from Company B will be substandard = P(S/B) = 0.03

Now, the probability of substandard aggregates is given by = P(S)

P(S) = P(A) [tex]\times[/tex] P(S/A) + P(B) [tex]\times[/tex] P(S/B)

= 0.7 [tex]\times[/tex] 0.05 + 0.3 [tex]\times[/tex] 0.03

= 0.044

Hence, the probability of substandard aggregates is 0.044.