Explaining Conditional Probability in Everyday Situations
Statistics and Probability · Flashcards
STATISTICS AND PROBABILITY · FLASHCARDS
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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
Find
P
(
A
)
P(A)
P
(
A
)
if
A
A
A
and
B
B
B
are independent,
P
(
A
∣
B
)
=
0.30
P(A\mid B)=0.30
P
(
A
∣
B
)
=
0.30
, and
P
(
B
)
>
0
P(B)>0
P
(
B
)
>
0
.
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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