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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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A gambler decides to play successive games of blackjack until he loses three times in a row. (Thus the gambler could play five games by losing the first, winning the second, and losing the final three or by winning the first two and losing the final three. These possibilities can be symbolized as LWLLL and WWLLL.) Let g n be the number of ways the gambler can play n games.
a. Find g 3 , g 4 , and g 5 .
b. Find g 6 .
c. Find a recurrence relation for g 3 , g 4 , g 5 , .

To determine

(a)

To find the value of g3, g4 and g5.

Explanation

Given information:

A gambler decides to play successive games until he loses three times in a row. Thus the gambler could play five games by losing first, winning the second and losing the final three or by winning the first two and losing the final three. These possibilities can by symbolized as LWLLL,WWLLL. Let gn be the number of ways the gambler can play n games.

Calculation:

For finding g3, the number of games that gambler can play is 3 games.

He can play 3 games only and only if he loses all these games. Suppose he wins any game he will play another game. So there is only possibility i.e. LLL. Hence the value of g3=1

To determine

(b)

To find the value of g6

To determine

(c)

To find the recurrence relation for g3, g4, g5,......

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