IFoA_CAA_M0 無料問題集「IFoA Module 0 - Entry」

In a small island nation, local sea vessels are identified using "a letter and 4 digits" classification system. The "letter" can be any of the 26 letters in the English alphabet, A to Z, while the "digit" can be any number from 0 to 9. E.g: Z9835.
Calculate the probability of a sea vessel having an identification ending in "007".

A geometric series is given by

Identify the values of x for which the series converges.

1/5 of actuarial students like skiing.
2/5of actuarial students like snowboarding.
1/3 of actuarial students like skiing and snowboarding.
Calculate the proportion of actuarial students that like skiing or snowboarding.
A)

B)

C)

D)

Using simple iteration, based on trial and improvement, the cubic equation below can be solved:
2x3 + 5x2 +7x - 12 = 0
Solve for x to 6 decimal places.

Calculate

A function f(x) is known for two values:
f(2) = 8 and f(5) = 14.
Using linear interpolation estimate f(3). A)

B)

C)

D)

A biased coin has the following probability distribution function: P(heads) = 0.80 P(tails) = 0.20
The biased coin is tossed twice in succession.
Calculate the probability of tossing at least one tail.