Chapter 13.5, Problem 40E

To determine

To explain: The statement of player that a roll of 10 is due to come up.

Answer to Problem 40E

It can't be stated that a move of 10 is expected to come up.

Explanation of Solution

Given information:

The game is that two number cubes are rolled and in past few rolls a sum of 10 has not turned up.

The statement of player is that a roll of 10 is due to come up.

Consider the provided information that the game is that two number cubes are rolled and in past few rolls a sum of 10 has not turned up. The statement of player is that a roll of 10 is due to come up.

Sample space of the event is $S=\left\{\begin{array}{cccccc}\left(1,1\right)& \left(1,2\right)& \left(1,3\right)& \left(1,4\right)& \left(1,5\right)& \left(1,6\right)\\ \left(2,1\right)& \left(2,2\right)& \left(2,3\right)& \left(2,4\right)& \left(2,5\right)& \left(2,6\right)\\ \left(3,1\right)& \left(2,3\right)& \left(3,3\right)& \left(3,4\right)& \left(3,5\right)& \left(3,6\right)\\ \left(4,1\right)& \left(2,4\right)& \left(4,3\right)& \left(4,4\right)& \left(4,5\right)& \left(4,6\right)\\ \left(5,1\right)& \left(2,5\right)& \left(5,3\right)& \left(5,4\right)& \left(5,5\right)& \left(5,6\right)\\ \left(6,1\right)& \left(2,6\right)& \left(6,3\right)& \left(6,4\right)& \left(6,5\right)& \left(6,6\right)\end{array}\right\}$

The rolls are autonomous. so regardless of whether a sum of 10 has not turned up in the previous barely any rolls, the result of the following roll is independent and hence he can't state a move of 10 is expected to come up.