Question

A six sided die is weighted so that the probabilities of rolling a 1, 2, or 3 are equally likely; the probabilities of rolling a 4, 5, or 6 are equally likely, and the probability of rolling a 5 is four times the probability of rolling a 3. What is the probability that a 2 or a 5 is rolled?

Answer 1

1=x
2=x
3=x
4=4x
5=4x
6=4x
so 15x=1 as sum of probabilities has to equal 1
therefore x=1/15

p(rolling a 2) = x
p(rolling a 5)=4*x

is that clear?

Answer 2

Yep, thank you!

Answer 3

You're welcome

Answer 4

It also seems intuitive that
Prob (1 or 4), Prob(2 or 5) and Prob(3 or 6) would all be equally likely and sum to 1.
Thus, each of these has a probability of 1/3