Sanderson M. Smith

THE GEOMETRIC SETTING Brad's poster provides an explanation of the geometric setting along with an example.

The geometric setting:

• Each observation falls into one of two categories: Success or Failure (or whatever you wish to call them).
• The probability of success is the same for each observation.
• The observations are independent.
• The variable of interest is the number of trials required to obtain the first success.

Brad's graphics display relates to the random variable x, where x is the number of times a single die must be rolled until a 6 occurs. Possible values for x are 1,2,3,4,......

Here are some of the probabilities displayed in Brad's chart.

 Value of x Probability 1 1/6 = 16.67% 2 (5/6)(1/6) = 13.89% 3 (5/6)2(1/6) = 11.57% 4 (5/6)3(1/6) = 9.65% 5 (5/6)4(1/6) = 8.04% 6 (5/6)5(1/6) = 6.70% 7 (5/6)6(1/6) = 5.58% 8 (5/6)7(1/6) = 4.65% 9 (5/6)8(1/6) = 3.88% 10 (5/6)9(1/6) = 3.23% 11 (5/6)10(1/6) = 2.69% 12 (5/6)11(1/6) = 2.24% 13 (5/6)12(1/6) = 1.87% 14 (5/6)13(1/6) = 1.56% 15 (5/6)14(1/6) = 1.30% 16 (5/6)15(1/6) = 1.08% 17 (5/6)16(1/6) = 0.90% 18 (5/6)17(1/6) = 0.75% 19 (5/6)18(1/6) = 0.63% 20 (5/6)19(1/6) = 0.52%