My maths is a bit rusty, can anyone help?

If A has a 90% chance of happening, B has a 80% chance of happening and C, 70%

Then the chances of A AND B happening are 90%*80% = 72%
and likewise for A AND C, 90%*70% = 63%

However what are the chances of A happening AND (either B OR C)?
What is the maths behind that one?

Ouch, mine's rusty too. Something to do with Bayes Theorem, I think.

Anyway, here's an 'interesting' page on probability that might help:

http://www.stats.gla.ac.uk/steps/glossary/probability.html

You have to think about it backwards: there are four combinations of B and C
1) B and C both happen
2) B happens but C doesn't
3) C happens but B doesn't
4) Neither B nor C happen.

You want to capture the first three cases (I assume by 'or' you mean 'OR' not 'XOR'), so the probability of that is 100% minus the probability that neither happen, which is 1-(.2*.3)=.94 or 94%. Then multiply by the probability of A (90%) to get A AND (B OR C) as 84.6%.

You could also do the same by summing the first three cases, but it takes longer that way.

[Edited by carl - 4/17/2002 11:19:40 AM]

I was gonna say that but Carl beat me to it! ;)

what if it rains? will it still happen?

that doesn't sound right to me.

if a and b have a 70% chance of happening
A and C have a 60% chance of happening how can the chances of either of these happeing together be MORE than the chance of one happening on it's own?

The chance of B OR C happening is far greater than the chance of one of them happening.

Matt you are saying what if A (AND) B happen Carl is saying if A ( OR ) B happen - totally different .....

its all to do with the OR statement

disagree - it says A and (B or C)

i.e. A and B and C would not count

therefore it's 90%x(24%+14%) = 34.2%

(B not C is 80% x 30% = 24%)
(C not B is 70% x 20% = 14%)

(generally in questions like this they're kept simple hence XOR is never used, they would have put 'and or' instead of 'or' if both B and C could apply in addition to A)

isn't maths fun! :)
Gordo

[Edited by Gordo - 4/17/2002 7:17:31 PM]

whichever way its read .. he now has all the possible answers he could of wanted !! :D