** Tossing pennies gets the binomial expansion
and probability/Chapter 9**

Don worked for a short time with Tadeo, in Argentina via IM in 2004 and 2005. Tadeo figured out how many ways 3 coins could come up-8. Don made an organized table below to show these:

In the table below we kept track of the
information above. So for **3** coins there would be **8** ways they could
come up. The 3rd row shows the information above, that there is **1** way for
3 Heads to come up, **3** ways for 2 Heads and 1 Tail to come up, **3**
ways for 1 Head and 2 Tails to come up, and **1** way for 3 Tails to come up-
**1 3 3 1 **in row 3, for a total of 8 ways they can come
up. Tadeo found some patterns in this triangle of numbers- known as Pascal's
triangle or Tadeo's triangle.

Don showed Tadeo another way to write this
information in the 3rd row below. Then he saw that if
the probability of getting a Head, H = 1/2 and
the probability of getting a Tail T= 1/2, then
the probability of getting 3 heads and 0 tails is 1***** (1/2)^{3}*****(1/2)^{0
}= 1/8.

Some other questions you could work on:

What is the probability, when you flip 3 coins, that you will get at least 2 Heads?

What is the probability, when you flip **5**
coins, that you will get exactly 3 Heads?

Make up other probability questions.

A new way to show statistics (using Gapminder.org) by Hans Rosling on TED

To other discoveries

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