Calculating probability that 5 dice rolls will produce an average of 3.5

Question

We are carrying out a dice game which involves 5 people rolling dice and passing buttons equal to the number rolled . We have to work out the probability that we will get an average of 3 .5 items passed along each turn. If any one would be able to help that would be great ?

Answer 1

The probability is 0. The average of five dice rolls is some integer divided by 5, but $3.5 = \frac72$ is not any integer divided by 5.

However, the average value of a dice roll is 3.5, so over a large number of turns the average of all throws will roughly equal 3.5.