B1. A bag contains two regularly shaped (cubic) dice which are identical in size. One die has the number 2 on every side. The other die has the numbers 2 on three sides and number 4 on each side opposite to one that has number 2. You pick up a die and look at one side of it, observing the number 2. What is the probability the opposite side of the die has the number 2 as well? Express your answer as an irreducible fraction.
Solution: There are 9 different sides we could be looking at: either side of the first dice, or 3 sides of the second dice. In 6 of those possibilities (i.e. for each side of the first dice), the other side is also a 2 , so the probability is $\frac{6}{9}=\frac{2}{3}$.
Answer: $2 / 3$.