excans:5655e8d0a9

Answer: C

The number of left-handed members at the end of each year [math]k[/math] is:

[math]L_{0}=75[/math] and [math]L_{1}=(75)(0.75)[/math]

Thereafter, [math]L_{k}=L_{k-1} \times 0.75+35 \times 0.75=75 \times 0.75^{k}+35 \times\left(0.75+0.75^{2}+\ldots 0.75^{k-1}\right)[/math]

Similarly, the number of right-handed members after each year [math]k[/math] is:

[math]R_{0}=25[/math] and [math]R_{1}=(25)(0.5)[/math]

Thereafter, [math]R_{k}=R_{k-1} \times 0.50+15 \times 0.50=25 \times 0.50^{k}+15 \times\left(0.50+0.50^{2}+\ldots 0.50^{k-1}\right)[/math]

At the end of year 5, the number of left-handed members is expected to be 89.5752, and the number of right-handed members is expected to be 14.8435 .

The proportion of left-handed members at the end of year 5 is therefore

[math]\frac{89.5752}{89.5752+14.8438}=0.8578[/math]

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.