I tried to work something out. Can anyone check whether this is correct?

1. probability of going bankrupt after 1 repetition = 0.52

2. probability of going bankrupt after 3 repetitions =

probability of going bankrupt after 1 repetition (0.52) + probability of going bankrupt after 3 repetitions (0.48*0.52*0.52). The result is 0.6498

3. probability of going bankrupt after 5 repetitions =

probability of going bankrupt after 3 repetitions (0.6498) + probability of going bankrupt after 5 repetitions (0.48*0.52*0.48*0.52*0.52)*2. The result is 0.7146

Ho do I calculate the probability of winning £2 after exactly 5 repetitions?

And what about the expected pay-out after each repetitions?

Thank you,

Fede