Question

Die A has 4 red faces and 2 black faces. Die B has 2 red faces and 4 black faces. A coin is flipped once. If it were heads, only die A is used (die B is discarded). If it were tails, only die B is used (die A is discarded). We do not get to know which die was chosen.

a) The first roll of the chosen die gives red. What is the probability that the second roll (with the same die) will be red?
b) The first two rolls of the die were both red. What is the probability that the third roll (with the same die) will be red?

Answer 1

a) 5/9

b) 1/3

Explanation:

a) P(Die A or Die B) = P(red and red with Die A) + P(red and red with Die B)

= 4/6 × 4/6 + 2/6×2/6

= 5/9

b) P(Die A or Die B) = P(red and red and red with Die A) + P(red and red and red with die B)

= 4/6×4/6×4/6 + 2/6×2/6×2/6

= 1/3