Difficult# Tossing a Weighted Dice

APSTAT-1TSN6P

A $6$-sided dice is weighted so that not every number is equally likely to appear when the dice is tossed. The table below shows the probability distribution.

Result (X) | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

p(X) |
0.12 | 0.14 | 0.08 | 0.27 | 0.25 | 0.14 |

Suppose the dice is tossed and we are told that the result is a number greater than $4$. Based on this information, what is the probability that the result was a $6$?