Losses covered by a flood insurance policy are uniformly distributed on the interval [0, 2]. The insurer pays the amount of the loss in excess of a deductible d.

The probability that the insurer pays at least 1.20 on a random loss is 0.30.

Calculate the probability that the insurer pays at least 1.44 on a random loss.

• 0.06
• 0.16
• 0.18
• 0.20
• 0.28

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: C

We have

[[math]] \begin{align*} 0.3 &= \operatorname{P}[ \textrm{insurer must pay at least 1.2} ] = \operatorname{P}[ \textrm{loss } \geq 1.2 + d] = \frac{2-1.2-d}{2-0} = \frac{0.8-d}{2} \\ d &= 0.8-2(0.3) = 0.2. \end{align*} [[/math]]

Then

[[math]] \operatorname{P}[ \textrm{insurer must pay at least 1.44} ] = \operatorname{P}[ \textrm{loss } \geq 1.44 + d] = \frac{2-1.44-0.2}{2-0} = 0.18. [[/math]]

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.