As an industrial engineer at Bluth’s Frozen Banana, you have two options to redu

Question

As an industrial engineer at Bluth’s Frozen Banana, you have two options to reduce on-handinventory: (i) develop a better demand forecasting model, and (ii) implement a differentpurchasing strategy. The likelihood that option (i) works (that is, reduces on-hand inventory) is 0.6. The likelihood that option (ii) works is 0.75. You choose to implement both options. Assume that both options function independently of each other.

a. What is the probability that both options were effective in reducing on-hand inventory?

b. What is the probability that neither option was effective?

c. What is the probability that at least one of the options was effective?

Explanation / Answer

Let A denote that function 1 works and B denote function 2 works.

a. P(A and B) = P(A)*P(B) = 0.6*0.75 = 0.45

b. P(neither A nor B) = 1 - P(A or B) = 1 - [P(A) + P(B) - P(A and B)] = 1 - [0.6 + 0.75 - 0.45]

= 0.10

c. P(at least one) = P(A or B) = P(A) + P(B) - P(A and B) = 0.6 + 0.75 - 0.45 = 0.90

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