let the number of accidents that occur in a year be X.Then we are given that
Poisson distribution follows a memoryless property therefore the probability that there will be an accident next year given there was no accident in last 6 months is equal to the probability of an accident in the next year without any condition.
Let be the number of accident in next year .Then we get:
Therefore we simply have to find:
Therefore poisson distribution probability formula we get:
Therefore 0.9699 is the required probability
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