propability?

For Jack and Paul get the same number of Tails as Paul,

Denote T be tail, H be head.

The possibilities are as followings:

a. Jack: T,T. Paul: T,T
b. Jack: T,T. Paul: T,H
c. Jack: T,T. Paul: H,T
d. Jack: T,T. Paul: H,H

e. Jack: H,T. Paul: T,T
f. Jack: H,T. Paul: T,H
g. Jack: H,T. Paul: H,T
h. Jack: H,T. Paul: H,H

i. Jack: T,H. Paul: T,T
j. Jack: T,H. Paul: T,H
k. Jack: T,H. Paul: H,T
l. Jack: T,H. Paul: H,H

m. Jack: H,H. Paul: T,T
n. Jack: H,H. Paul: T,H
o. Jack: H,H. Paul: H,T
p. Jack: H,H. Paul: H,H


There are totally 16 possibilities. The red fonts represent the events that meet the requirements. There are totally 6 events fulfil the conditions.

So, P(Jack gets the same number of tails as Paul)
= 6 / 16
= 3 / 8


2007-06-02 11:07:31 補充：
For a more convenient method:P(Jack gets the same number of tails as Paul)= P(Jack:T,T and Paul T,T) P(Jack:T,H and Paul:H,T) P(Jack:H,H and Paul H,H)= (1/2 X 1/2) X (1/2 X 1/2) (2 X 1/2 X 1/2) X (2 X 1/2 X 1/2) (1/2 X 1/2) X (1/2 X 1/2)= 1/16 1/4 1/16= 3/8