Question

what would the expected annual profit be for an insurance company
if The company charges an annual premium of $110 for minor
injuries. Actuarial Studies show that in case of an injury claim
the company will Pay out an average of $900 for outpatient care in
an average of $3000 for an overnight stay in the hospital they also
determined on average each year there are five claims made that
result in outpatient care for every 1000 policies and three claims
made that result in an overnight stay out of every 1000 polities.
What is the expected annual profit of an insurance policy for the
company????

Answer #1

Data as per the information given:

Scenerio | x | P(x) | x* P(x) |

no injuries | 110 | 0.992 | 109.12 |

outpatient care | -790 | 0.005 | -3.95 |

overnight stay | -2890 | 0.003 | -8.67 |

Total | Total | 1.000 | 96.50 |

In case of no injuries co gets = 110 ; Prob = 992/1000 = 0.992

In case on outpatient care claim, co gets = 110 - 900 = -790 ; Prob = 5/1000 = 0.005

In case on overnight stay claim, co gets = 110 - 3000 = -2890 ; Prob = 3/1000 = 0.003

Expectecd value = X * P(X)

Expectecd value = (0.992 * 110) + (0.005 * -790) + (0.003 * -2890) = 96.50

**ANS: Expectecd value = 96.50**

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