Question

Mario and Bowser begin with a hat that has 5 balls in it: 3 are red, 2 are green. Bowser secretly picks a ball and tells Mario it is red, although he might be lying about the color. If there is an 80% chance Bowser is lying, what is the probability that Mario draws 2 red balls in a row after Bowser's initial draw?

Answer 1

1) probabillity of getting two red balls in a row is 1/2 (if 80% Bowser is lying)
2) probability of getting 2 red balls in a row is 1/6 (20% Bowser's truth)
3)  overall probability $( \frac{4}{5} * \frac{1}{2}) + (\frac{1}{5} * \frac{1}{6}) = \frac{13}{30}$