Q. Claim in an insurance company occurs at the rate of 1 per year. Find the probability that a claim will occur in the next one year.
Ans. 1-e –¹×¹ = 0.6321 or 63.21%
Isn’t it counter intuitive that probability of next claim is 63.21% when claims occur at the rate of 1 per year?
The claim rate given is an average rate which is computed historically. Where data set might include some year with no claim and some year with more than 1 claim.
Lambda is average rate of occurrence of event.
Therefore the probability given is so.