O'Reilly logo

Illuminating Statistical Analysis Using Scenarios and Simulations by Jeffrey E. Kottemann

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

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 img 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.

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 252/1024ths 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 ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required