Question for deep thinkers, not just Mathematicians?

Question

If there is 10% chances/odds of a particular event to happen then is it true that in 100 chances (all other variables being the same) the event would occour ten times definately - or could it happen that in a hundered chances the event occours only 4 or 5 times Despite having 10% chances/odds?

Answer 1

'In theory' it would happen 10/100 times but this isn't guarrenteed. All it means is that there is a 10% chance of it happening there and then. It doesn't mean that if its happened 9 times and you're about to do the 100th go, that it will happen. It still has a 10% chance of happening no matter what happened before it.

Answer 2

The event in question will most likely occur 5-15 times. It is not at all unusual for it to transcend that range (it may even occur every time or not occur at all). However, as you increase the repetitions the odds, consequently, hold greater significance. If you have 100 repetitions the event may occur more or less than the given odds. Ex. you flip a coin 100 times: you may very well get heads 55 times and tails 45 times or even 60-40 with a percent variance of 20% (10/50 x 100%). Let us repeat this coin flip 100,000 times. The odds are the law in this scenario and most likely you will see heads no more or no less than 49-51 percent (49,000 - 51,000 times) or a percent variance of 2% (1/50 x 100%). Even in science for an experiment to be validated it must be repeated time and time again in the same exact fashion to have any credibility. Finally let us take a look at some extremes. You flip a coin twice: the odds state that you sholud see both head and tails once each. In this case however the odds are weak and of little significance. At the other end of the spectrum flip a coin 500,000,000,000,000 times and I absolutely guarantee without a doubt (after rounding the tens of thousanths spot in the decimal) you will have 50% heads and 50% tails. On a side note always keep in mind that the last event has no bearing on the next event and the odds reset. Luck is to defy the odds and consequently luck is obsolete in the long run.

Answer 3

It could happen that in a hundred chances the event occours only 4 or 5 times Despite having 10% chances/odds.

Probability is the likelihood of an event occurring, not the driving cause of an event.

Answer 4

Understand that when you say "there's a 10% chance of...", you are assuming that someone has already inferred from past sampling that the event in question occurs in 10% of the cases sampled. The information that is not present is the degree of confidence the experiment was designed to approach.

As a basic example, suppose that the person telling you that the event occurs 10% of the time drew his experience from an experiment designed to give him 65% confidence in his answer. Now how would you feel about taking the 10% "to the bank", as they say?

In real life, you would never get a "there's a 10% chance of this happening" from a real statistician without him/her telling you the confidence interval (e.g., with 95% confidence) of the result. The lower that percentage (or the bigger the +/- gap when they say 10% +/- x%), the less confidence you would have in the situation described above (in a sample of 100 draws, obtain exactly 10 positive results).

Answer 5

you best bet to get the true understanding of this is by using the binomial theorem and the normal z distribution.
n=number of trials =100
p=probability of something happening=.1
q=probability of p not happening= .9
mean= n X p = 100 X .1 = 10
standard deviation = the square root of n X p X q

now things will vary around 10 +or - for each sample of 100
we will see how the distribution falls for an outcome of 2 and 18
this will give us a range around 10.

2-10/ sqrt 100 x .1 x .9 = -8/3 = z= -2.6667 =.0038
for 18 it would be the compliment of this z=2.6667 =..9962
get the jist. you can figure out the whole distribution now. remember the denominator will be the same and SD =3
0, 20 = z= +/- 3.33 = .0004
1, 19 = z= +/- 3.00 = .0013
2, 18 = z= +/- 2.667 =.0038
3, 17= z= +/- 2.333 =. .0099
4, 16 = z= +/- 2.000 = .0228
5, 15 = z= +/- 1.667 = .0475
6, 14 = z= +/- 1.333 = ..0934
7, 13 =z = +/- 1.000 = .1587
8, 12 = z= +/- .667 = ..2514
9, 11 =z= +/- .333 = ..3707
10= z= 0 = .500

remember, the probabilities in the right column are cummulative, so you can subtract the number after for each outcome. the exact probability for each outcome is below.
i'll do it for you. to get exactly a 10 is just under 1 chance in 4.

0,20 = .0004
1,19,= (.0013 --.0004= .0009) do you get the jist?
2,18 = .0025
3,17 = .0061
4, 16 = .0129
5,15 = .0247
6, 14 = .0459
7,13 = .0653
8,12 = .0927
9,11 = .1193
10 = .1293X2=.2586

there are your probabilities for each outcome. It works out as adding up all probabilities for each outcome adds up to 1.

gl

Answer 6

There is a chance that the 10% probability could happen 100 times - in fact, there is a .1^100 chance that it will.

You can find the chances of any number of occurrences happening by looking at the equation (.9 + .1)^100. Clearly this is equal to 1, since .1 + .9 = 1. The nth term gives you the probability of the event occurring n times: the chance of it occurring 0 times is .9^100, the chance of once is P(100, 1)*.9^99*.1^1.

The chance of its occurring exactly 10 times, then, is P(100, 10)*.9^90*.1^10, which by my calculator is about 0.13186534682448858. So you see that far from having to occur exactly 10 times, it will occur 10 times only about once in 7 trials.

Answer 7

Statistics is meaningful only over a large number of event draws. I would hardly say that repeating 100 times the same basic draw is enough to give a statistically significant result, under the assumption that the resulting event is YES or NO. You'd have to go much further than that (say, 10,000 for example) to start getting results that make sense, and you'd still probably get close to the predicted probability but not exactly there. There's a test called CHI Squared that provides you with a measure of the confidence you can have upon the results you get, though. It can speed up the verification of validity of a particular statistics.

Answer 8

No If p(x)=10% then p(notx)=p(y)= 90% the event space is (X+Y)^100 so C X^10 Yx^90= p(the event would occour ten times ), its to late to calculat it but it ~10%

Answer 9

Ten % chances means that in the long run (trials tending to infinity) the limit of the ratio chances/odds is 10%
By NO MEANS the event must appear 10 times in 100trials .It even could not appear at all.

Answer 10

It could happen any number of times up to 100. It is possible for it to not happen in 100 chances, as well as happen all 100 times.

What chance tells us is the probability of one event occuring. It does not tell us how many positive instances there will be in a given number. That cannot be produced definitively in ideal conditions.

However, if this were to be tested out, after thousands and thousands of chances, the number of positive instances creep closer and closer to the 1/10th mark.