Experiment: roll a pair of 6-sided dice.

LetE be the event that the sum of the two dice is 5.

LetF be the event that the first die rolls a 1.

E and F are independent.

Suppose you are rolling weighted dice.The dice are weighted so that rolling a 1 has a different probability from the other 5 numbers (which are all equally likely).Both dice are weighted identically, and it is possible to roll any of the 6 results on each die. What are the probabilities of the 6 possible results of one of these dice?