# probability of Independent events help.

• Jan 5th 2013, 09:33 PM
FriendofOrion
probability of Independent events help.
The probability of any unrelated events occurring together in the same period.

Now for the Mathematical probability of these events happening independently of each other. Here is the logic. If each event above is considered as an event on its own and not related to another event mentioned above and if this event has 2 possibilities; it happens or it doesn't happen. The probability of the event on its own would be 1/2 or 0.5. Now, if we consider another event which has the same probability, that is 0.5 and we then consider the probability of both of these events occurring on or very near the same time, then according to probability theory then the resulting probability of both events occurring would the the product of the 2 probabilities. This would give the result of 0.5 multiplied by 0.5 which would equal 0.25(or 1 in 4). If n was the number of 'co-incidental events', then the collective probability of ALL of these events occurring in the same time period would be 0.5 to the power of n.

To put this in perspective, see the table of results below.

No of events Probability
********************************
10 1 in 1024
15 1 in 32768
20 1 in 1,048,576
25 1 in 334,455,342
30 1 in 1,073,741,824 {with this probability, a perhaps person may buy only one lotto ticket in their life and win the jackpot!!!!!!!!]
32 1 in 4,294,967,296

Is this mathematical logic correct? It appears to me that it is.
• Jan 5th 2013, 10:41 PM
chiro
Re: probability of Independent events help.
Hey FriendofOrion.

What are the time periods that these can occur on: Are the ticks discrete time (finite number of ticks) or continuous time (infinite number of points on timeline)?
• Jan 6th 2013, 12:33 AM
FriendofOrion
Re: probability of Independent events help.
I think it would be continuous time.`Say within a day or a few weeks from each other. I'm trying to get some measure of the probability of a series of events that some would say are co-incidental. For example if a man was on trial for the murdering his wife and the court prosecutor pointed out that the mans business was failing, he was having an affair with another woman and he had recently taken out a life Insurance policy on his wife and she is subsequently murdered. What is the probability that all 3 events should occur within a short time period? The probability becomes very remote as the number of events increases in number.
I hope that helps