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What is the probability that if 1,000,000 people flipped a coin that only 100 would be heads.?

I’m assuming each one of the 1,000,000 people are flipping their own coin, not each on of them flips the same coin, and no chance of any rigged coins.

This is a simple application of the binomial theorem.

————– ————– ————– ————–

Let’s break it down on a smaller scale for a moment. Say there are 5 people and you only want 2 heads. The probability of heads is 1/2, and of tails is 1/2 too. So one possible outcome:

P ( H H T T T ) = (1/2) (1/2) (1/2) (1/2) (1/2) = 1/32

The probability of every outcome with 2 heads and 3 tails is 1/32 since you would simply rearrange them:

P ( H T H T T ) = (1/2) (1/2) (1/2) (1/2) (1/2) = 1/32

But how many different combinations of 2 heads and 3 tails are there? That’s the real question, and the answer is:

5C2 = the binomial coefficient “5 choose 2″

You can compute 5C2 = 5! / (2! 3!) = 10

Since this is a “smaller” version of the big problem, you could actually list all 10 of them:
H H T T T – 1
H T H T T – 2
H T T H T – 3
H T T T H – 4
T H H T T – 5
T H T H T – 6
T H T T H – 7
T T H H T – 8
T T H T H – 9
T T T H H – 10

That means that you have 10 scenarios, each with probability 1/32. That makes the total probability 10/32 = 5/16, which is 0.3125 as a decimal.

————– ————– ————– ————–

Now we must apply that on a MUCH larger scale. However, the application is EXACTLY the same.

You have a million flips, so each possible scenario will have probability of:

1 / 2^(1,000,000)

You want 100 heads (and 999,900 tails), which means the total number of scenarios you’re counting is:

1,000,000 C 100

The total probability is:

(1,000,000 C 100) / 2^(1,000,000)

That’s actually a pretty succinct way to express this fraction. It might be nicer to keep it that way than try to expand it out as a fraction, which would take pages and pages to display. However, what you probably want is a decimal form, so plug your expression into the calculator and get this approximation:

1.07691775 × 10 ^ (-300588)

That’s an EXTREMELY small fraction (virtually impossible).

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The hobby of coin collection can benefit people of all ages. As a hobby, which has been there since 1800, but lasted only for 1900. People collect coins for a variety of reasons from those who are interested in coins solely for the personal satisfaction of those whose motto is just making money through your collection. We are describing here the following general categories:

1. Professional Coin Collectors: These are the people collecting coins in order to get benefits sometime in the future. Most of the time they are pretty informed individuals who can assess the value of currencies by examining their conditions. They have the ability to separate a valuable coin from a lot of currency.

2. Investors: Collect coins exclusively as an investment. They are on the look out for rare types of coins. One can, of course, finding high-value coins – coins that are older, limited edition coins, coins in circulation, and the rare types of coins by accident, but it's hard to have the possibility of discovery for the collection. So I often buy these coins from anyone willing to sell, particularly of professional currency traders. A coin collector of investors differs of a professional coin collector largely on the degree of specialization.

3. Currency traders: While it is highly debatable, but coin dealers also form a separate category of coin collectors. Always watching for rare types of coins of value. In general, do not keep their currencies to the long, compared with other coin collectors who are trying to build a collection over a period of time. Most dealers currency would have a quick turn – are sold as fast as possible for quick profits.

4. Fans: These are people who collect coins exclusively for personal fulfillment and pleasure. Amateur usually a larger vision behind his hobby – love of money, are interested in knowing their stories, etc. Quite often, the fans to donate his collection of coins history museums or other organizations. And sometimes happens in his collection to the generation next and so on. While fans start collecting the coins only to fulfill their personal interests, to later start times profit.

5. Crown coin collectors are those who start collecting coins themselves but inherited the collection of the generation Last week (s). In general, the heirs only maintain the collection of coins, but treasure, but do nothing, and passed to the next generation. Sometimes the heir is interested in collecting and growing even more.

6. Hoarder: These are people just keep coins what it finds. Some simply have fear of losing a coin of value if not stored. They are neither responsible, non-profit nor gather because of the love of coins – are nothing more than profiteers. Many hoarders can turn around, examine and evaluate your collection for his courage, others usually do not worry.

Well, these are the categories noramlly known collctors currency – in one extreme is the professional coin collector who is an expert, and in others, it only stores the Horder coins.You can calculate for yourself which category belong.

About the Author:

Abhishek is an avid Coin Collecting enthusiast and he has got some great Coin Collecting Secrets up his sleeve! Download his FREE 58 Pages Ebook, “Understanding And Mastering The Art Of Coin Collecting!” from his website http://www.Fun-Galore.com/92/index.htm . Only limited Free Copies available.

Article Source: ArticlesBase.com – 6 Coin Collector Types – How They Collect Coins