There are two dice and a player need to roll them at the same time and sum up the value of two dice. However, if the two dice give the same value, the player need to roll it again until the value of the two dice are different. The question is: what is the probability that the player getting a sum of 7 eventually?
Please help on this dice rolling problem??
- Thread starter yiuhang
- Start date
The distribution of roll sums after this process is
[MATH]\left( \begin{array}{cc} 3 & \frac{1}{15} \\ 4 & \frac{1}{15} \\ 5 & \frac{2}{15} \\ 6 & \frac{2}{15} \\ 7 & \frac{1}{5} \\ 8 & \frac{2}{15} \\ 9 & \frac{2}{15} \\ 10 & \frac{1}{15} \\ 11 & \frac{1}{15} \\ \end{array} \right) [/MATH]
You can see this by removing the rolls (1,1), (2,2), etc. and tabulating the results of the rest.
As seen the probability of getting a 7 is \(\displaystyle \dfrac 1 5\)
[MATH]\left( \begin{array}{cc} 3 & \frac{1}{15} \\ 4 & \frac{1}{15} \\ 5 & \frac{2}{15} \\ 6 & \frac{2}{15} \\ 7 & \frac{1}{5} \\ 8 & \frac{2}{15} \\ 9 & \frac{2}{15} \\ 10 & \frac{1}{15} \\ 11 & \frac{1}{15} \\ \end{array} \right) [/MATH]
You can see this by removing the rolls (1,1), (2,2), etc. and tabulating the results of the rest.
As seen the probability of getting a 7 is \(\displaystyle \dfrac 1 5\)
