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2.4. Fermats game. A and B compete against each other with a pair of dice. A wins if he rolls a total of 6, while B wins ifHint. One way to solve the problem is by an infinite series. If A denotes a game that A wins and B denotes a game that B wins

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a.Probability A wins if he rolls a total Possible outcomes if a gets sem of 6 = 4(1,5), (2,4), (3,3), (4,22,65 Probability of A- Possible Sequences -D-A D-ABC BCA - O ABBACA -SEXDATE) - A 28°ACABBA - (202) GUGGEG) (3) -^n%3CACABBAA -GEGY EBD - Total SaSom od @ 0,0 = 1) a)3CÍ r- 30 10003639) T-1811273072 1365 1 368 + (31)(30)3 (362)136°) – (31) (36) 364 = 5 [36+ (31)(30²) 364 - (31²) (30²) - 372780 0.4575 814716 - Probability of I

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