An insurance company charges its policy holders an annual premium of $200 for the following type of injury insurance policy. If the policy holder suffers a "major injury" resulting in lengthy hospitalization, the company will pay out $15,000 to the injured policy holder. If the policy holder suffers a "minor injury" resulting in significant absence from work, the company will pay out $4,000 to the injured policy holder. If no injury is encountered (the most probable event) the company, of course, does not payout anything to the policy holder.
Past records show that each year, 1 in every 2000 policy holders experience a "major injury" and 1 in every 500 experience a "minor injury.." Assuming that the only company expense related to this policy is the annual payout.
1. Construct a probability distribution table for "X" where "X" refers to the annual profit for this policy, where "X" = Annual Premium - Annual Payout.
2. Compute the expected annual profit that the company can expect to receive per policy holder.
1/2000= 0.0005 produces a payout of - $14800.00
1/500= 0.002 = 4/2000 produces a payout of -$3800
399/400= 0.9975= 1995/2000 profits
Question One
Probability table is a follows
X----(neg)14800---(neg)3800--200
P(x)-1/2000-------4/2000-----1995/2000
Question two
Expect Value= mean= Sum of (frequency* probability)
(-14800*(1/2000))+(-3800*(4/2000))+(200*(1995/2000)= 184.5 Annual profit for each individual policy holder.
To construct a probability distribution table for "X," where "X" refers to the annual profit for this policy, we need to calculate the probability of each outcome and the associated profit.
Let's denote:
M = Major injury
m = Minor injury
N = No injury
1. Probability distribution table for "X":
Outcome (O) Probability (P) Profit (X)
M 1/2000 $15,000 - $200
m 1/500 $4,000 - $200
N 1 - P(M) - P(m) $0 - $200
To calculate the probabilities:
P(M) = 1/2000
P(m) = 1/500
P(N) = 1 - P(M) - P(m)
Now, let's calculate the profits for each outcome:
Profit(M) = $15,000 - $200
Profit(m) = $4,000 - $200
Profit(N) = $0 - $200
2. To compute the expected annual profit that the company can expect to receive per policy holder, we multiply each profit by its corresponding probability and sum them up:
Expected Profit = (Profit(M) * P(M)) + (Profit(m) * P(m)) + (Profit(N) * P(N))
Substituting the values from above:
Expected Profit = ((($15,000 - $200) * 1/2000) + (($4,000 - $200) * 1/500) + (($0 - $200) * (1 - P(M) - P(m)))
Simplifying this expression will give you the expected annual profit that the company can expect to receive per policy holder.