Chapter 16 Events and Probability Spaces520
car locationA
B
C
A B C A B C A B C
player’s
intial
guessB
A
A
B
A
C
A
C
B
C
C
B
door
revealedoutcome.A;A;B/
.A;A;C/
.A;B;C/
.A;C;B/
.B;A;C/
.B;B;A/
.B;B;C/
.B;C;A/
.C;A;B/
.C;B;A/
.C;C;A/
.C;C;B/
Figure 16.3 The tree diagram for the Monty Hal Problem with the outcomes la-
beled for each path from root to leaf. For example, outcome.A;A;B/corresponds
to the car being behind doorA, the player initially choosing doorA, and Monty
Hall revealing the goat behind doorB.