1.3.22 Go back and take another look at Problem 2.29 from Chapter 2. For ease of notation, let us rename the numbers 5,10,...,100 on the wheel as 1,2,...,20.

For any a = 1,2,...,20, let S

(a) denote the probability of candidate A winning if candidate A stops after the first spin giving a score of a points and let C(a)

denote the probability of candidate A winning if candidate A continues after the f

irst spin giving a score of a points. Use conditional probabilities to find first an expression for S

(a) andnextanexpressionforC(a).Derivefromtheseexpressions the optimal stopping rule for candidate A andthemaximalprobabilityofcandidate A winning. Repeat the calculations for the case where the numbers 1,2,...,100 are on the wheel rather than the numbers 1,2,...,20.