Need help determining which formula to use

Greetings,

I'm not a math buff and Google has failed to help me find a mathematical formula. I'm hoping someone here can help me out or point me in the right direction.

I'm trying to determine how to calculate the probability of something happening. The scenario is this... I'm playing a game and one of my characters has a 20% chance of his skill working. If he attempted the skill twice, what is the actual percent chance of the skill working at least once? I realize it's greater than 20% because he's attempted it twice, but I'd like to know how to calculate it specifically.

One more twist... If there are diminishing returns on this skill working, would that be a different formula? For example, the first two attempts at using the skill his chance is 20%, then the third attempt the chance of success is reduced to 10% and on the fourth and final attempt he only has a 5% chance.

So, to summarize:

What is the chance of an event happening at least once in two attempts if each attempt only has a 20% chance of success?

What is the chance of an event happening at least once in four attempts if the first two attempts have a 20% chance of success, the third attempt has a 10% chance and the fourth and final attempt has a 5% chance of success.

Thank you very much for any insights you can provide (I've been trying to find this for days now, so you're my last hope of not going crazy trying to answer this...)

Be well.

ecoladd said:

Greetings,

I'm not a math buff and Google has failed to help me find a mathematical formula. I'm hoping someone here can help me out or point me in the right direction.

I'm trying to determine how to calculate the probability of something happening. The scenario is this... I'm playing a game and one of my characters has a 20% chance of his skill working. If he attempted the skill twice, what is the actual percent chance of the skill working at least once? I realize it's greater than 20% because he's attempted it twice, but I'd like to know how to calculate it specifically.

One more twist... If there are diminishing returns on this skill working, would that be a different formula? For example, the first two attempts at using the skill his chance is 20%, then the third attempt the chance of success is reduced to 10% and on the fourth and final attempt he only has a 5% chance.

So, to summarize:

What is the chance of an event happening at least once in two attempts if each attempt only has a 20% chance of success?

What is the chance of an event happening at least once in four attempts if the first two attempts have a 20% chance of success, the third attempt has a 10% chance and the fourth and final attempt has a 5% chance of success.

Thank you very much for any insights you can provide (I've been trying to find this for days now, so you're my last hope of not going crazy trying to answer this...)

Be well.

Click to expand...

The chance of it not working the first time is 80%. The chance of it not working the second time is 80%. The chance of it not working either time is .8*.8=.64, so the chance of it working at least one of the times is .36 (36%). In general, the chance of something working 1 of n times is 1-(1-p)^n, where p is the probability of it happening on one occurrence.

If the odds are changing, it works similarly in your example it would be 1-(.8*.8*.9*.95), using the odds of it not working for each term. That comes to 45.28%.

If you want the odds of it happening 2 times of four or such, say so, and I will explain that function as well.


ETA: basically, you are work out the odds of it not happening n times in a row, then subtract that from 100%

Wow, awesome! Thank you so much for the speedy and clear response, much appreciated!!

(now back to my game to see where to allocate my character's energy to optimize his results)

Have a great weekend.