Question

Jack and Jill keep rolling a six-sided and a three-sided die, respectively. The first player to get the face

having just one dot wins, except that if they both get a 1, it’s a tie, and play continues. Let N denote

the number of turns needed. Find:

a. P(N=1), P(N=2).

b. P(the first turn resulted in a tie|N = 2).

c. P(Jack wins).

Answer #1

a)

When Jack gets 1 and Jill gets other than 1 on the first turn or Jack gets other than 1 and Jill gets 1 on the first turn, the game ends on the first turn.

The probability that the games ends on the first turn is

The probability that the games ends on the second turn is

b) The conditional probability

c) For Jack to win, Jill should not win. The game continues on tie and when Jack gets faces 2,3,4,5,6 and Jill get faces 2,3.

The probability Jack wins on the turn is

The probability Jack wins is

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