Question

suppose that we roll four fair six-sided dice.
a) What is the conditional probability that the first die shows 2, conditional on the event that exactly three dice show 2?

b) What is the conditional probability that the first die shows 2, conditional on the event that at least three dice show 2?

Thank you.

Answer 1

for each one, the first die is NOT dependent on any of the other three dice

the other three dice do NOT affect the outcome of the first die

Answer 2

so you can ignore the part "conditional on the event that exactly three dice show 2"

and just focus on "What is the probability that the first die shows 2". Notice how I erased "conditional"