Alex and Beth take turns flipping a pair of coins. The first person to flip a pair of heads wins the game. Alex flips first. Beth eventually wins. What is the probability she flipped a pair of heads on her second turn?
Can someone verify if this reasoning is correct or not:
Question can be converted to Bayes rule:
P(someone wins given that they don't flip first) = 3/7 (solved the equation p=(.75)(.25) + (.75)(.75)(p))
Desired probability: P(Beth wins on 2nd turn | she wins and Alex flips first) = (.75)(.75)(.75)(.25)/(3/7)
This equals approximately 1/4.