A factory needs two raw materials, say, A and B. The probability of having an adequate supply of material A is 0.94, whereas the probability of having an adequate supply of material B is 0.96. A study shows that the probability of a shortage of both A and B is 0.02. What is the probability that the factory has a shortage of either material A or B?

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Hint: work with the probabilities of shortage of A, B, A∩B, and from the three, calculate A∪B.

To find the probability of a shortage of either material A or B, we can use the principle of inclusion-exclusion.

Let's denote the probability of a shortage of material A as PA, and the probability of a shortage of material B as PB. We want to find the probability of PA ∪ PB (the union of A and B).

PA = 1 - probability of adequate supply of material A = 1 - 0.94 = 0.06
PB = 1 - probability of adequate supply of material B = 1 - 0.96 = 0.04

Now, we need to find the probability of a shortage of both A and B, which is given as 0.02.

We can use the formula for the union of two events:
P(PA ∪ PB) = P(PA) + P(PB) - P(PA ∩ PB)

P(PA ∩ PB) is the probability of both A and B being in shortage, which is given as 0.02.

Therefore:
P(PA ∪ PB) = 0.06 + 0.04 - 0.02
P(PA ∪ PB) = 0.08

So, the probability that the factory has a shortage of either material A or B is 0.08, or 8%.