Question

An insurance company is issuing 16 independent car insurance policies. If the probability for a claim during a year is 15 percent, what is the probability (correct to four decimal places) that there will be more than two claims during the year?

Answer 1

Solution

Given that ,

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X > 2) = 1 - P(X 2)

= 1 - P(X = 0) - P(X = 1) - P(X = 2)

= 1 - (₁₆ C ₀) * 0.15⁰ * (0.85)¹⁶ - (₁₆ C ₁) * 0.15¹ * (0.85)¹⁵ - (₁₆ C ₂) * 0.15² * (0.85)¹⁴ ​​​​​​​

= 0.4386

Probability = 0.4386