Question

There is a 5% chance that someone gets into a car accident in a month.

If they do, the insurance company pays out $10,000.00

The insurance cost $1200.00

Construct a probability distribution and find the expected values?

x	P(x)

Expected Value=

Answer 1

There is a 5% chance that someone gets into a car accident in a month.

i.e Probability that someone gets into a car accident in a month = 5/100 =0.05

if they do, the insurance company pays out $10,000.00

The insurance cost $1200.00

X : net Payout

X = $10,000 -$1200 = 8800  if someone gets into a car accident in a month

P(X=8800) = Probability that someone gets into a car accident in a month = 0.05

Insurance cost = $1200 i.e net payout = -$1200 if there was no car accident

Probability of no car accident = 1-0.05 =0.95

P(X=-1200) = Probability of no car accident =0.95

x	P(x)
8800	0.05
-1200	0.95

Expected Value = E(X)

Expected Value = -$700