Illuminating Statistical Analysis Using Scenarios and Simulations

4Judging Coins II

Let's revisit Statistical Scenario–Coins #1, now with additional information on each of the possible outcomes. Table 4.1 summarizes this additional information. As noted, there are a total of different unique patterns of heads & tails possible when we flip a coin 10 times. For any given number of heads, as we have just seen, there are one or more ways to get that number of heads.

Statistical Scenario—Coins #2

Using Table 4.1, where do you draw the two lines for declaring the coin to be unfair?

Table 4.1 Coin flipping details.

#Heads	#Ways	Expected relative frequency	Probability	as Percent	Rounded
0	1	1/1024	0.00098	0.098%	0.1%
1	10	10/1024	0.00977	0.977%	1.0%
2	45	45/1024	0.04395	4.395%	4.4%
3	120	120/1024	0.11719	11.719%	11.7%
4	210	210/1024	0.20508	20.508%	20.5%
5	252	252/1024	0.24609	24.609%	24.6%
6	210	210/1024	0.20508	20.508%	20.5%
7	120	120/1024	0.11719	11.719%	11.7%
8	45	45/1024	0.04395	4.395%	4.4%
9	10	10/1024	0.00977	0.977%	1.0%
10	1	1/1024	0.00098	0.098%	0.1%
Totals:	1024	1024/1024	1.0	100%	100%

The #ways divided by 1024 gives us the expected relative frequency for that number of heads expressed as a fraction. For example, we expect to get 5 heads 252/1024^ths of the time. The fraction can also be expressed as a decimal value. This decimal value can be viewed as the probability that a certain number of heads will come up ...