Question

In: Statistics and Probability

Two players A and B play a dice game with a 6-face fair dice. Player A...

Two players A and B play a dice game with a 6-face fair dice. Player A is only allowed to roll the dice once. Player B is allowed to roll the dice maximally twice (that is, Player B can decide whether or not she or he would roll the dice again after seeing the value of the first roll). If the player with the larger final value of the dice wins, what is the maximal probability for Player B to win the game?

Solutions

Expert Solution

1)If player A rolls 1.

Then Player B can win if it rolls a number from 2 to 6. Now it has two chances, either he can win on the first roll. If not then it may win in the second roll.

Hence the probability of B winning is

2) If Player A rolls 2:

Then Player B can win if it rolls a number from 3 to 6. Now it has two chances, either he can win on the first roll. If not then it may win in the second roll.

Hence the probability of B winning is

3) If player A rolls 3

Then Player B can win if it rolls a number from 4 to 6. Now it has two chances, either he can win on the first roll. If not then it may win in the second roll.

Hence the probability of B winning is

4) If player A rolls 4:

Then Player B can win if it rolls a number from 5 and 6. Now it has two chances, either he can win on the first roll. If not then it may win in the second roll.

Hence the probability of B winning is

5) If player A rolls 5:

Then Player B can win if it rolls a number 6. Now it has two chances, either he can win on the first roll. If not then it may win in the second roll.

Hence the probability of B winning is

6) If player A rolls 6:

Player B cannot win here, as there is no number greater than 6 on the dice.

Hence the maximal probability for Player B to win the game=

orchestra answered 1 year ago
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