Help! quick maths help needed

[Greebo]

My brain is failing me today and I quickly need the answer to the following.

In the next 18 months there are 7 months of importance. I know for sure that 4 other important things will occur in the next 18 months.

What is the probability that one of the 4 things coincide with one of the 7 months of importance.

Needs a quick answer, help please. Greatly appreciated.

 

[Greebo]

Just to clarify as I may not have explained it properly.

There will be 7 important months in the next 18. This is a 100% certainty. The only thing not known is which 7.

There will also be 4 other different important events cropping up in the next 18 months. This is also 100% certainty.

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.

It does not matter if more than one occurs eg all 4 coincide or just 3 or 2. Just need to know if at least one does.

Gut feeling is that multiplying is wrong as the answer is too low.....

 

[Greebo]

Ye gads.

It's easier to work out the probability of it not occurring - which is (11/18) to the power 4 - and subtracting that from 1.

So your probability of one or more conflicts is 86%

That's looking favourite so far and makes sense. ANy more confimations that this is the right answer please?

 

[Greebo]

Oh, also, does it matter if any of the 4 other important things coincide with each other?

That would make it 1-(11/18)(10/18)(9/18)(8/18) = 92%

Yes it does. Never thought of that. None of the 4 events can occur in the same month.

 

[Greebo]

Let's look at a similar problem. Suppose you have two coins and you flip them, what's the probability that they will both be heads?

I think it's the same type of problem. You got 1/2 chance of the first coin coming out heads (i.e. 7/18 months) and again 1/2 chance of the second one (i.e. 4/18). To find the answer you need to multiply. I stand by my answer which comes at around 8.6%.

No. It's more like the old problem of what are the odds if you have 30 people in a room together that two people have exactly the same birthday. Most people work it out to be really low. The actual answer is near enough 50% which surprises most people.

(this assumes that every day is just as likely to be somebodies birthday which in real life isn't true is AUgust/September has the highest birthrates - xmas and new year "accidents" plus major power cuts cause peaks as well )

 

[Greebo]

Ye gads.

It's easier to work out the probability of it not occurring - which is (11/18) to the power 4 - and subtracting that from 1.

So your probability of one or more conflicts is 86%

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) ?

as once you have the probability that the first event didn't coincide you only have 10 months of the 17 months left for the 2nd event to occur in.

Or am I over analysing this?