Expert: Sherry Wallin - 10/20/2011

Question
To Miss Wallin:

This question happens on  popular game show sometimes-"The Price is Right."

Situation-2 players. You go first.

Game-spin a wheel has 20 spots on it from 5,10,15 up to 100. You spin first-goal is to
get to 100 without going over. If go over-automtically lose. You can only spin twice.

If you are first-what number after you first spin-should you stop on. And let the other
player try to beat you. It is obviously a gigantic advantage to go last-as you will play
perfect strategy.

Side note-if you and opponent happen to tie-say both got 80. Then have a 1 game spin-off
to see who has the highest amount.

 I know the first person who spins-must hit/and stop on one of the numbers below after
the first spin. If so which one is it? Also thru my calculations if must go first in this contest-
using optimun strategy will win around 32% of the time. Is this correct?

So if must go first in this contest-what figure to hit/and stop on after the 1st spin.

Hit 50/stick 55
Hit 55/stick 60
Hit 60/stick 65
Hit 65/stick 70

It has to be one of the 4 possibilites above-that I know.

Thanks for any insight.  And if my example was not clear enough-will try again.

Answer
Timothy it would help me if you were to tell/show me what techniques you used to arrive at your conclusions. Every number has a 1/20 chance of being hit and every pair of numbers (sum) has a 1/20^2 chance of occurring. How many of these sums would cause a failure?? i.e. a sum over 100?
If you are the first spinner it is necessary to know these values in order to  determine your chance of win/lose at least with respect to not being disqualified for a sum over 100. Once you calculate those numbers use conditional probability to determine the 'best' choice of when to stop on the first spin or 2nd spin if you spin first. Let the event A be the number on your first spin and B be the event that you get less than or equal to 100. Then find P(B|A) = P(A Intersect B)/P(A).

You show me what you did to arrive at your conclusions and I will show you if you did it right and tell you what else you might need to do.
Note I haven't addressed all your questions as I am awaiting more information.

Math Prof