Answer :
The probability that a company ships by truck or rail or both is 0.89 or 89%.
We can solve this problem by using the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
where A and B are two events.
In this case, we want to find the probability that a company ships by truck or rail or both, which is equivalent to the probability of the union of the two events "shipping by truck" and "shipping by rail". Let T denote the event "shipping by truck" and R denote the event "shipping by rail".
From the problem statement, we know:
P(T) = 0.82
P(R) = 0.47
P(T and R) = 0.40
Using these probabilities, we can calculate:
P(T or R) = P(T) + P(R) - P(T and R)
= 0.82 + 0.47 - 0.40
= 0.89
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