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What is the lowest acceptable probability number beyond which it would considered impossible?
Answer 1: Borel's Law tells us that anything with a probability less than 1 in 1050 is "mathematically impossible." Leslie Orgel calculated that any event that has one chance in just 10^50 (1 followed by 50 zeros) is dismissed by mathematicians as never happening. Mathematician William Dembski's calculations can be summed up with the following simplification of the primary principle: "If you roll a 6 sided die, one time, what are the chances that you will roll a 7 or higher?" The correct answer is that it's impossible. Thus, the resulting number can not exceed the afforded chances.
Answer 2: An impossible event is if there is a 0% chance of it occurring. If you were to flip a coin until you got 'cheese' as a result, then there is a 0% chance, it is not possible.
Above 0, nothing is impossible, they just have greater and greater degrees of improbability. Tossing 25 coins and getting 10 heads in a row for example is 1/33554432 or 0.00000298% which sounds impossible. But if you got 33,554,432 people to simultaneously flip 25 coins each, in theory one person should get 25 heads.
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What is the probability of a girl getting pregnant if hymen is not broken and guy doesn't release sperm?
The probability is quite low, BUT it isn't zero, and this is a very risky practice. Human nature being what it is, the intention not to break the hymen and not to release sperm is one of those intentions that lead to Hell (so to speak). Beyond that, there is the risk of various diseases that is not in the least diminished.
Importance of probability in life?
I can not give you a simple answer. It is very individual and subjective. I will assume that you are referring to probability theory. Statistics is based on an understanding of probability theory. Many professions require basic understanding of statistics. So, in these cases, it is important. Probability theory goes beyond mathematics. It involves logic and reasoning abilities. Marketing and politics have one thing in common, biased statistics. I believe since you are exposed to so many statistics, a basic understanding of this area allows more critical thinking. The book "How to lie with statistics" is a classic and still in print. So, while many people would probably say that probability theory has little importance in their lives, perhaps in some cases if they knew more, it would have more importance.
What is data extrapolation?
An extension or projection beyond the limit of the data is extrapolation.
What percentage of a normal distribution is located in the tail beyond z equals 2.00?
2.27%
Measurements that fall beyond 3 standard deviations from the mean?
They do happen, particularly with very skewed distributions.
