Conditional Probability and Independence
Statistics and Probability · Flashcards · Application
STATISTICS AND PROBABILITY · FLASHCARDS
Card 1
of 20
0 got it
0 to review
Current
Got it
Still learning
Not seen
QUESTION
Identify the error: A student writes
P
(
A
∣
B
)
=
P
(
A
∪
B
)
P
(
B
)
P(A\mid B)=\frac{P(A\cup B)}{P(B)}
P
(
A
∣
B
)
=
P
(
B
)
P
(
A
∪
B
)
. What is the correction?
QUESTION
Find
P
(
B
∣
A
)
P(B\mid A)
P
(
B
∣
A
)
if
A
A
A
and
B
B
B
are independent and
P
(
B
)
=
0.15
P(B)=0.15
P
(
B
)
=
0.15
.
QUESTION
Decide whether
A
A
A
and
B
B
B
are independent:
P
(
A
)
=
0.5
P(A)=0.5
P
(
A
)
=
0.5
,
P
(
B
)
=
0.4
P(B)=0.4
P
(
B
)
=
0.4
,
P
(
A
∩
B
)
=
0.2
P(A\cap B)=0.2
P
(
A
∩
B
)
=
0.2
.
Tap to flip before you grade
ANSWER
Independent, since
P
(
A
∩
B
)
=
P
(
A
)
P
(
B
)
=
0.2
P(A\cap B)=P(A)P(B)=0.2
P
(
A
∩
B
)
=
P
(
A
)
P
(
B
)
=
0.2
. Checks if
P
(
A
∩
B
)
=
P
(
A
)
P
(
B
)
P(A\cap B)=P(A)P(B)
P
(
A
∩
B
)
=
P
(
A
)
P
(
B
)
:
0.2
=
0.5
×
0.4
0.2=0.5\times 0.4
0.2
=
0.5
×
0.4
✓.
Swipe → got it · swipe ← still learning
Got it
Still learning
Flip Card
Previous card
Next card