A company has five employees on its health insurance plan. Each year, each employee independently has an .80 probability of no hospital admissions. If an employee requires one or more hospital admissions, the number of admissions is modeled by a geometric distribution with a mean of 1.50. The numbers of hospital admissions of different employees are mutually independent. Each hospital admission costs 20,000. Calculate the probability that the company’s total hospital costs in a year are less than 50,000.

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Barbara Klein · Accepted Answer

Step 1If anyone has made any number of hospital visits, they have       1    3   chance of making at least one more visit, and a       2    3   chance that this is their last visit.Going through the cases:No one files a claim   (  0.80      )    5  One person files one claim.Step 21 of 5 people goes to the hospital. They only have one visit.  (  0.80      )    4    (  0.20      )    1                                (                            5        1                              )                      (      2    3    )2 claims are filed1 claim each by 2 different people  (  0.80      )    3    (  0.20      )    2                                (                            5        2                              )                      (      2    3        )    2  2 claims by 1 person.  (  0.80      )    4    (  0.20      )    1                                (                            5        1                              )                      (      1    3    )  (      2    3    )and sum them all up.

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