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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A=0.06

B=0.04
A∩B=0.02
by the inclusion/exclusion principle,
A∪B=(0.06+0.04)-0.02=?

To find the probability that the factory has a shortage of either material A or B, we need to first find the probability of a shortage of A, the probability of a shortage of B, and then subtract the probability of a shortage of both A and B.

Let's calculate each of these probabilities step-by-step:

1. Probability of a shortage of A (denoted as P(A)):
The probability of having an adequate supply of A is given as 0.94. Therefore, the probability of a shortage of A can be calculated as:
P(A) = 1 - P(adequate supply of A)
= 1 - 0.94
= 0.06

2. Probability of a shortage of B (denoted as P(B)):
The probability of having an adequate supply of B is given as 0.96. Therefore, the probability of a shortage of B can be calculated as:
P(B) = 1 - P(adequate supply of B)
= 1 - 0.96
= 0.04

3. Probability of a shortage of both A and B (denoted as P(A ∩ B)):
The probability of a shortage of both A and B is given as 0.02.

Now, we can calculate the probability of a shortage of either A or B by using the Inclusion-Exclusion principle:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = 0.06 + 0.04 - 0.02
= 0.08

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