SOA Exam P Sample Question 108
Study guide: Exam P-1
In a certain game of chance, a square board with area 1 is colored with sectors of either red or blue. A player, who cannot see the board, must specify a point on the board by giving an x-coordinate and a y-coordinate. The player wins the game if the specified point is in a blue sector.
The game can be arranged with any number of red sectors, and the red sectors are designed so that R_i = \left(\frac{9}{20}\right)^i, where R_i is the area of the i^{\text{th}} red sector.
Calculate the minimum number of red sectors that makes the chance of a player winning less than 20%.
- A) 3
- B) 4
- C) 5
- D) 6
- E) 7
Answer this question and see the worked solution