The Game Show Problem. You are on a game show, given the choice of 3 doors. Behind one is ... Note: The proof shows that the preference probability (and its linear ...
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Yuval Shahar, M.D., Ph.D.
A
B
= P(A)+P(B)P(A)*P(B) = P(A)+P(B)  P(A & B)
A
B
A & B
=
=
P(A
&
B)
P(A)P(B

A)
P(B)
P(A

B),
P
(
B
)
P
(
A

B
)
=>
=
P
(
B

A
)
P
(
A
)
For example, for diagnostic purposes:
+
P
(
D
)
P
(
T

D
)
=
=
+
P
(
disease

test
:
positive
)
P
(
D

T
)
+
P
(
T
)
If a random variable X can take on discrete values Xi with probability P(Xi ) then the expected value of X is
If a random variable X is continuous, then the expected value of X is
1/16 *
= 1/16 * 6 = 6/16 = 3/8
P
1
La
Lb
1P
Lc
B is the Certain Equivalent of the lottery < La, p; Lc, 1p>
Decision Rule: Prefer intelligence if IQ gap > 10, else experience