Page 211 - Probability Demystified

200 CHAPTER 11 Game Theory

Hence, the player (defence) should defend against the run 11 of the
19
time.
2. Let p be the probability of selecting a pistol and 1 p be the prob-
ability of selecting a rifle.

0:5p þ 0:3ð1 pÞ¼ 0:2p þ 0:8ð1 pÞ

0:5p þ 0:3 0:3p ¼ 0:2p þ 0:8 0:8p

0:2p þ 0:3 ¼ 0:6p þ 0:8

0:2p þ 0:6p þ 0:3 ¼ 0:6p þ 0:6p þ 0:8

0:8p þ 0:3 ¼ 0:8

0:8p þ 0:3 0:3 ¼ 0:8 0:3
0:8p ¼ 0:5

0:8p 0:5
¼
0:8 0:8
5
p ¼
8

5
The value of the game when p ¼ is
8

5 5
0:5p þ 0:3ð1 pÞ¼ 0:5 þ 0:31
8 8

5 3
¼ 0:5 þ 0:3
8 8

17
¼
40
5
When Player A selects the pistol of the time, he will be successful 17
8 40
of the time.