Calculating Overall Odds

Question

If you have a game that increases in difficulty with each turn, you'll have different odds of winning each turn. But how do you mathematically calculate overall odds? For example:

Round 1: 100% chance to win the round
Round 2: 90% chance to win the round
Round 3: 80% chance to win the round
Round 4: 70% chance to win the round
Round 5: 60% chance to win the round

But with every round, if you lose, the whole game is over. Playing 1 round is a sure thing. Playing two rounds it is possible to lose. Play 5 rounds and you are very likely to lose.

It works out to be a 60% chance of 70% of 80% of 90%. Is there some sort of algorythm that would give you the cumulative odds of winning a six round game? The result would be less than 60% because you could have lost on one of the previous rounds.

Calculating it the way I described it feels like a horribly inefficient brute-force method. There's got to be an elegant formula for this.

Answer 1

Can't we multiply all odds cause to win all 6 rounds we have to win each of them so winning first round and winning second round........
So there is and so we can multiply them to find answer
1*9/10*8/10*7/10*6/10*5/10
=15120/100000
=15.12%
Is it right or I get something wrong??

Answer 2

Seems rigth to me

Answer 3

I had trouble applying the suggestion, but I think I was inspired enough to work it out. Please check the code and see if you have any suggestions / corrections. Thank you @YUGRAJ.

https://code.sololearn.com/cA11A8A0A9a1