Conditional Dice Probability

P(B|A) with dice examples

P(Even | Roll Greater Than 3)

Question

If you rolled a die and were told the result is greater than 3, what is the probability that it was an even number?

✓

Let A = "roll greater than 3" = {4, 5, 6}

Let B = "even number" = {2, 4, 6}

We want P(B|A) = P(even | greater than 3)

Given roll greater than 3:

Numbers that are both greater than 3 AND even:

Answer

Unconditional

Conditional

Knowing the roll is greater than 3 increases our probability of even from 50% to 66.67% because 2 out of 3 high numbers are even (4 and 6).