Question

A certain board game uses two standard six-sided dice. Each player rolls the dice and advances a number of squares equal to the sum of the values on the dice. If the player rolls doubles (two dice with the same value) on the first roll, the player is allowed to roll again. Similarly, if he rolls doubles on the second roll, he is allowed a third roll. If he rolls doubles on the third roll, he receives a penalty. What is the probability that a player will receive such a penalty on any given turn?

Answer 1

The probability that a player will receive such a penalty on any given turn is P=0.0046 or 1 chance in 216.

Explanation:

Each roll involves two six-sided dice.

If we get the same value in both dice, the player is allowed to roll again.

We will have a penalty if we get the same value in both dices three times in a row.

First, we have to calculate the probability of getting the same value in both dices.

The possible outcomes are 6^2=36. There are only 6 numbers, so there are only 6 possible outcomes that have the same value.

Then, the probability of this event is:

`p=(6)/(36)=(1)/(6)`

Now, we can calculate the probability of having this event three times in a row. This can be calculated as:

`P=p^3=\left((1)/(6)\right)^3=(1)/(216)\approx 0.0046`