Text Problems are from Sheldon Ross, A First Course in Probability
(6th edn).
Problems (pp. 173ff)
7
14
19
33
45
49
73
(Be sure to explain your answer for 49 in detail)
Exercises (pp. 184ff)
3
5
20
Another Problem
One popular strategy for gambling on roulette, the martingale,
works as follows, for a gambler who starts with a stake of $15. In the US
roulette wheels have 38 equally-likely outcomes, 18 each
Red and Black and two Green
(European wheels have 37 outcomes, with only one Green). The martingale strategy is:
Bet $1 on Red. If Red
appears (US probability 18/38), quit with winnings $1. Otherwise,
Bet $2 on Red. If Red
appears (US probability 18/38 again), quit with winnings -$1+$2=$1.
Otherwise,
Bet $4 on Red. If Red
appears, quit with winnings -$1-$2+$4=$1. Otherwise,
Bet $8 on Red. If Red
appears, quit with winnings -$1-$2-$4+$8=$1. Otherwise,
Quit anyway with total winnings -$1-$2-$4-$8=-$15. Hitchhike home.
Let X denote the gambler's winnings (which could be negative!)
when she quits.
Find P[X>0].
Are you convinced that the strategy is indeed a ``winning''
strategy? Explain your answer.
The queen of England is said to have a net worth of about 400
million dollars. If she commits to play until she either wins once, or
loses it all, what is her expected winnings?