SOLUTION: A large city dating agency finds that their dating introductions result in the marriage of the matched-up clients at an average rate of 2 per year. The agency gives a special we

Question 1122600: A large city dating agency finds that their dating introductions result in the marriage of the matched-up clients at an average rate of 2 per year.
The agency gives a special wedding present to each pair of clients who marry.
Let X be the random variable for the number of marriages between the agency's clients that take place in a year.
For each question below, pick the formal probability statement that is equivalent to the probability required. Note that in some cases you will have to think about how the complement rule would be used to calculate the required probability.
The probability that at least 5 pairs of the agency's clients marry each other in a given year.
Answer 1
The probability that less than 5 pairs of the agency's clients marry each other in a given year.
Answer 2
The probability that one pair of the agency's clients marry each other in a given year.
Thank you so much in advance
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
P(X>=5) or, since this is a Poisson distribution, with parameter =2, 1-P(X<=4)
The second term is 0.9473
Probability 5 or more is complement or 0.0527
P(X <=4) or P(X<5) This is 0.9473 from above
P(X=1). This is 0.2707.
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