A purchasing agent placed rush orders for a particular raw material with two dif

Question

A purchasing agent placed rush orders for a particular raw material with two different suppliers, A and B. If neither order arrives in four days, the production process must be shut down until at least one of the orders arrives. The probability that supplier A can deliver the material in four days is 0.55. The probability that supplier B can deliver the material in four days is 0.35. a. What is the probability that both suppliers will deliver the material in four days? Because two separate suppliers are involved, we are willing to assume independence. What is the probability that at least one supplier will deliver the material in four days? What is the probability that the production process will be shut down in four days because of a shortage of raw material (that is, both orders are late)? b. c.

Explanation / Answer

P(A) = 0.55
P(B) = 0.35

a)
P(A and B) = P(A) * P(B)
= 0.55 * 0.35
= 0.1925

b)
P(A or B) = P(A) + P(B) - P(A and B)
= 0.55 + 0.35 - 0.1925
= 0.7075

Required probability = P(A or B) = 0.7075

c)
Required probability = P(A' and B')
= 1 - P(A or B)
= 1 - 0.7075
= 0.2925

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