Simple Game of Chance...

[thijs02]

I have a gambling-style game. I have found that I have exactly 3% chance of losing every time I play. If I play 100 rounds of this game, how big is the chance that I have lost a round? I thought it might be (1-0.03)¹⁰⁰, but I'm not sure.

 

[firemath]

Reworded: Are you asking if you have the chance of losing one game only or at least one game?

 

[thijs02]

Reworded: Are you asking if you have the chance of losing one game only or at least one game?

Yeah, sorry, I should clear that up. I'm talking about losing at least one game.

 

[Cubist]

You're close to the answer.

0.03 is the probability of losing in one game
(1-0.03) is the probability of NOT losing in one game
(1-0.03)¹⁰⁰ is the probability of NOT losing in ALL of 100 games

Now, what can you do to the last line in order to find the probability of losing at least once in 100 games?

 

[thijs02]

You're close to the answer.

0.03 is the probability of losing in one game
(1-0.03) is the probability of NOT losing in one game
(1-0.03)¹⁰⁰ is the probability of NOT losing in ALL of 100 games

Now, what can you do to the last line in order to find the probability of losing at least once in 100 games?

Whoops, yeah, I understand that. So it's 1-(1-0.03)¹⁰⁰?

 

[Cubist]

So it's 1-(1-0.03)¹⁰⁰?

Indeed, well done! It works out at roughly 0.95 or 95%