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so it's a pretty simple question but I am stumped, help anyone?

The first question was: i. Find the probability that it will rain on any particular day in August.

^We are given the mean number of days of rain for August (10.4) and I understand to get the answer you do 10.4 divided by 31 ( probability = 0.34 )

But what I don't know how to do is this question: ii. What is the probability that it will rain on two consecutive days in August?

I've tried but I'm not too sure what number I use with the mean to get the answer? The answer says probability is 0.12

All replies are greatly appreciated!

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    $\begingroup$ This is a bad question. It should specify that one is to assume that raining on one day is independent of raining on any other day, which is counter to the physical reality. $\endgroup$ – Fengyang Wang Oct 20 '14 at 1:17
  • $\begingroup$ This accepted answer is real life is not accurate. For example, suppose it starts raining at 11:55 PM on Aug 5th. What then would be the chance that it would stop raining by midnight only 5 minutes away on Aug 6th? Compare that to if it starts raining at 12:05AM on Aug 6th, what then would be the chances of it raining on Aug 7th? My point is rain on 2 consecutive days are related to each other, not independent of each other. If we had more information like the time it started raining on each of those days and the duration of the rain, then we might get a more accurate prediction. $\endgroup$ – David Oct 20 '14 at 1:52
  • $\begingroup$ This method might not be accurate enough however with the information given, this being only the mean, well it certainly gets the answer I needed, and works just as well for other similar questions so I'm satisfied with the answer, as it solved the problem :) $\endgroup$ – Daisy Oct 20 '14 at 2:31
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Try to think about it as any other problem that you have already worked with. If the probability of a certain event is $0.34$, what is the probability that this event occur two times in a row? $(0.34)\times(0.34) = 0.1156$ that is approximately $0.12$.

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We are to find the probability of rain for 2 consecutive days in the month of August. It is given that the Mean number of days of rain for August is 10.4. So, the probability of rain for 2 consecutive days means - (10.4/31)x((10.4/30)=0.1163 or 0.12; i.e. 2 consecutive days refers to 31 days and 30 days.

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