Chances of Losing 10 times in a row with specific percentages.

Question

The following betting has a 60% chance of losing (lose everything), 38% chance of winning (win double what was bet), and 2% chance to triple your winnings (instead of doubling). I have enough money to place down a $1 bet and continually double down ($2, $4, $8... $512) ten times. What is the chance that I'll lose all ten times in a row?

 

I understand that this is probably an easy question, however, I'm asking here instead of figuring it out myself. If I could get the work, that would be amazing as well. Thank you for your troubles.

Answer 1

p(LOSS) = 0.6

 

P(10 consecutive losses) = 0.6¹⁰ = 0.00605