Help! quick maths help needed

[ntg]

How about we pick an example which isn't entirely misleading? And actually bares some resemblance to the OP's problem. Try this one: you're going to toss two coins and see whether either of them come up tails. This is much closer to the original question because it's asking for one or more, rather than all of.

See end of this post please. I think you got it wrong and I also want to highlight that your post comes across impolite.

Multiplying the chances is absolute mathematical garbage akin to trying to work out 3+6 by appending the digits to get 36.

Yes, that's entirely correct. It's absolutely nothing to do with the problem you've been asked to solve though.

So which one is it? is it mathematical garbage or is it entirely correct? Multiplying and adding probabilities is the cornerstone of probability theory, not something I made up.

(edit) What you've actually worked out is the a priori probability that both will fall in any given month without knowing what happened in all the other months; which is clearly different from what is asked.

Which is what the OP asked, quoting from his "clarification post":

Therefore I am trying to find out what the chance is that any one of the 7 important months coincides with one of the 4 important events.

If that isn't asking for the probability of two events coinciding out of the same sample then I don't know what is.

 

[DaveF]

Thinking about it because none of the 4 events can occur in the same month, shouldn't it be

1- (11/18 * 10/17 * 9/16 * 8/15) ?

Yes.

Number of ways of arranging the 4 events over 18 months (ignoring your 7 bad months) is 18P4 = 18 x 17 x 16 x 15.
Number of ways arranging the events over the 11 good months = 11P4 = 11 x 10 x 9 x 8

So P(no clash) = 11P4/18P4 = 11/18 x 10/17 x 9/16 x 8/15.

 

[DaveF]

See end of this post please. I think you got it wrong and I also want to highlight that your post comes across impolite.

His first answer was correct, the 2nd (accounting for events not lying in the same month) was incorrect, but not massively.

So which one is it? is it mathematical garbage or is it entirely correct?

It's garbage.

Multiplying and adding probabilities is the cornerstone of probability theory, not something I made up.

Addition is one of the cornerstones of arithmetic too, but that doesn't mean it's writing (a/b)+(c/d) = (a+b)/(b+d) is anything but garbage.

If that isn't asking for the probability of two events coinciding out of the same sample then I don't know what is.

You seem rather confused about what your actual events are here. What you've basically done is calculate the probabilty that two events will coincide in one particular month. But we need the probability of them coinciding in any of the 18 months.

(And since the 18 events "there is a clash in month N" (N = 1,..., 18) are not disjoint or independent, it would be very difficult to fix this; multiplying your answer by 18, for example, gives an incorrect answer).