Help with Probability Equation

Question

I'm trying to put together an app for fun that has a scenario where I need to figure out a probability equation for the following scenario:

Suppose I have a number of attempts at something and each attempt has a success rate (known ahead of time). What are the odds after doing all those attempts that a success happens?

For example there are three attempts (all will be taken individually).

The first is known to have a 60% success rate. The second is known to have a 30% success rate. The third is known to have a 75% success rate. What are the odds of a success occurring if all three attempts are made?

I've tried several formulas and can't pinpoint the correct one.

Thanks for the help!

Answer 1

The likelihood of winning is equal to the likelihood of not losing all three: 1 - (1 - 0.6) (1 - 0.3)(1 - 0.75)

.4 *.7 *.25 = 1

To put it another way, find the likelihood that all of your attempts will fail and reverse it. So, given a finite sequence of occurrences with probabilities P[i], the probability that at least one of them would succeed is 1 - P[i] (1 - P[0]) * (P[1] - 1) *... * (1 - P[n])

And here's a perl one-liner to compute the value: (input is white-space separated list of success rates)

 perl -0777 -ane '$p=1; $p*=1-$_ foreach @F; print 1-$p . "\n"'