Thread: How do you calculate your chances after multiple attempts?

A video game related question I've been trying to figure out all night long.

A Shotgun has a 10% chance to land a critical hit. What's your chance of landing a critical hit after firing the gun 10 times? I know this does not mean you have a 100% chance because you could theoretically shoot 11-20+ times before finally landing one (lower odds but it'll happen). Is there a way of calculating these odds?

Now I could do this myself by firing 10 shots a thousand times. Determine how many batches of 10 got critical hits and how many didn't to determine an average success rate. But there's got to be a formula for this.

1/10 x 10 = 100% (incorrect)
1 x 10 / 10 x 10 = 10% (incorrect)

I know its not 100% and you have a much higher chance then 10%. I remember long ago I had a similar problem involving a Roulette wheel in Phantasy Star Universe (if it had no zeroes.) No matter how many times red or black comes up (in a row) you still have a 50% of winning on the next spin no matter what color you pick. But the probability of black appearing 5 times in a row is MUCH higher then it appearing 500 times in a row. But I wasn't able to calculate the odds of that happening.

Thanks very much for your time and for reading this post. And my deepest apologies if its on the wrong sub-forum or if the title was not descriptive enough (^_^ ;; )

Originally Posted by Galactimus

A video game related question I've been trying to figure out all night long.

A Shotgun has a 10% chance to land a critical hit. What's your chance of landing a critical hit after firing the gun 10 times? I know this does not mean you have a 100% chance because you could theoretically shoot 11-20+ times before finally landing one (lower odds but it'll happen). Is there a way of calculating these odds?

Now I could do this myself by firing 10 shots a thousand times. Determine how many batches of 10 got critical hits and how many didn't to determine an average success rate. But there's got to be a formula for this.

1/10 x 10 = 100% (incorrect)
1 x 10 / 10 x 10 = 10% (incorrect)

I know its not 100% and you have a much higher chance then 10%. I remember long ago I had a similar problem involving a Roulette wheel in Phantasy Star Universe (if it had no zeroes.) No matter how many times red or black comes up (in a row) you still have a 50% of winning on the next spin no matter what color you pick. But the probability of black appearing 5 times in a row is MUCH higher then it appearing 500 times in a row. But I wasn't able to calculate the odds of that happening.

Thanks very much for your time and for reading this post. And my deepest apologies if its on the wrong sub-forum or if the title was not descriptive enough (^_^ ;; )

Probability of all missing is (0.9)^10

CB

So a 65% chance of getting 1 (or more) critical hits in 10 shots. Thank you very much for your assistance. (^_^)v