Ralph Vince - Portfolio Mathematics

ch01 JWBK035-Vince February 22, 2007 21 : 43 Char Count= 0

The Random Process and Gambling Theory 11

Finally, for 10 coins:

Combination Probability

H10 .001 *

H9T1 .01 **********

H8T2 .044 *****(45 different ways)

H7T3 .117 *****(120 different ways)

H6T4 (^205) (210 different ways)
H5T5 .246 (252 different ways)
T6H4 .205 (210 different ways)
T7H3 .117 (120 different ways)
T8H2 .044 *(45 different ways)
T9H1 .01 **
T10 .001 *
Notice thatas the number of coins increases, the probability of get-
ting all heads or all tails decreases.When we were usingtwo coins, the
probability ofgettingall heads or all tails was. 25 .For three coinsit was
.125, for four coins. 0625 ;for sixcoins.0156, and for 10 coinsit was. 001.

Possible Outcomes and Standard Deviations

So a coinflipped four times has a total of 16 possible exact sequences:

1. HHHH

2. HHHT

3. HHTH

4. HHTT

5. HTHH

6. HTHT

7. HTTH

8. HTTT

9. THHH

10. THHT

11. THTH

12. THTT

13. TTHH

14. TTHT

15. TTTH

16. TTTT