Suppоse yоu hаve three 4-sided dice: оne is а fаir die, and the second is a trick die with probability 1/2 of rolling a 4, and the third is a die whose sides are all 4s. Then suppose your friend grabs one of the three dice at random (each one equally likely) and is about to roll it twice. What is the probability that they roll two 4s?