valleeny wrote:Hi Testluv
The problem becomes more complicated if thr probability of raining is not equal to the probability of not raining = 1/2. In this case I don't think you can simply use (total desired events/total possible outcomes)?
?
Well, as I posted above, in that case it is best to approach the problem the way you first posted in this thread.
We're still sticking to the logic of the formula although you might say we're not using it directly; that is we're not
contradicting the formula; we're just multiplying the number of ways the desired event can occur by the appropriate probability weighting. If you're asking me whether there is a way of doing it directly with the formula in one shot when the probability of rain and not rain is not equal, then, no, I don't know a way to do that.
When the probability is 1/2, no matter if we want 2, 3, 4 rainy days, we will always be raising 1/2 to 5, and so, approaching it the way you did in your first post, you will always come out with 1/32. (Of course, then we multiply by the appropriate number of ways, which we can get either from the nCk formula or the triagnle). For example, if we want rain exactly 2 days, then again we have (1/2)^2 * (1/2)^3, and because we are multiplying the same bases, we add the exponents, and we'll have (1/2)^5. But if we want rain on just 1 day, then we'll have (1/2)^1 * (1/2)^4, and again we'll have (1/2)^5. But if the probability of the desired event is anything other than 1/2, when we multiply (des) * (undes), we will always have different bases, and so the math is a lot more protracted.