Explaining Conditional Probability in Everyday Situations
Statistics and Probability · Flashcards · Recall
STATISTICS AND PROBABILITY · FLASHCARDS
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QUESTION
Which probability describes "chance of being a smoker if you have lung cancer":
P
(
C
∣
S
)
P(C\mid S)
P
(
C
∣
S
)
or
P
(
S
∣
C
)
P(S\mid C)
P
(
S
∣
C
)
?
QUESTION
Which statement is correct:
P
(
A
∣
B
)
=
P
(
B
∣
A
)
P(A\mid B)=P(B\mid A)
P
(
A
∣
B
)
=
P
(
B
∣
A
)
always, or they can differ?
QUESTION
Identify the error: "If
P
(
A
∣
B
)
P(A\mid B)
P
(
A
∣
B
)
is high, then
P
(
B
∣
A
)
P(B\mid A)
P
(
B
∣
A
)
must be high."
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ANSWER
It confuses
P
(
A
∣
B
)
P(A\mid B)
P
(
A
∣
B
)
with
P
(
B
∣
A
)
P(B\mid A)
P
(
B
∣
A
)
; they can differ greatly. Common fallacy: conditional probabilities aren't symmetric.
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