You, Annie, and Bob will be participating in a truel (a duel with 3 people). The three of you will take turns firing one shot from your gun; once a person is hit he/she is out of the competition. You have the advantage of going first, but you only hit your intended target 30% of the time. Annie goes next, and she never misses. Bob shoots third, and he hits his intended target 50% of the time. What should your strategy be as the first shooter? (Assume a rotation of You, Annie, Bob, You, Annie, Bob, etc. until one person is hit, afterwhich the two remaining competitors take turns shooting.)

Sometime ago I bought that book you have referred, someone borrowed from me and I lost it as happen frequently with lended books. I believe its author is someone call Frederick Hosteller or alike, and I do remember more or less the solution of this particular problem, so it will be unfair from me to write about it, and spoil the fun of others.

It is a really entertaining book, even for me who do not like too much the field of probability. In that book I remember a problem referred to a drowry which almost obsessed me, I did spend hours and hours mulling over it, in my commuting driving, awaiting my flight in airports,or just awake in my insomnia,it was really challenging experience, so if you consider appropiate post it, I believe you should get a lot of attention.

See

https://www.maa.org/mathland/mathtrek_1_26_98.html

for a discussion and a couple of additional references.