SOLUTION: Question During rush periods, accidents happen in Nicosia at a rate of 2 per hour. The morning rush period lasts for 1 hour 30 minutes, and the evening rush period for two hours.

Question 1058329: Question
During rush periods, accidents happen in Nicosia at a rate of 2 per hour. The morning rush period lasts for 1 hour 30 minutes, and the evening rush period for two hours.
1. What is the probability that there will be no accidents during the morning rush period?
2. What is the probability of 2 accidents during the evening?
3. What is the probability of four or more accidents during the morning?
4. What is the probability that there will be no accidents during both the morning and evening rush period?

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
We use the Poisson probability(P) distribution
:
Probability ( x, u ) = (e^(-u) * u^x) / x!, where u is average number of successes, x is actual successes, e is approx 2.71828
:
1) P ( x = 0 ) = (e^-3) * 3^0) / 0! = 0.0498
:
2) P ( x = 2 ) = (e^-4) * 4^2) / 2! = 0.1465
:
3) P ( x > or = 4 ) = 1 - summation i = 0, 3 of P (x = i ) with u = 3
P ( x = 0 ) = 0.0498
P ( x = 1 ) = 0.1494
P ( x = 2 ) = 0.2240
P ( x = 3 ) = 0.2240
P ( x > or = 4 ) = 1 - 0.6472 = 0.3528
:
4) P ( x = 0 ) where u = 7 is 0.0009
:

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