Databricks
DATABRICKS-CERTIFIED-PROFESSIONAL-DATA-SCIENTIST · Question #108
Suppose A, B , and C are events. The probability of A given B , relative to P(|C), is the same as the probability of A given B and C (relative to P ). That is,
The correct answer is A. P(A,B|C) P(B|C) =P(A|B,C). From the definition, P(A,B|C) P(B|C) =P(A,B.C)/P(C) P(B.C)/P(C) =P(A,B.C) P(B,C) =P(A|BC) This follows from the definition of conditional probability, applied twice: P(A,B)=(PA|B)P(B)
Statistics and Probability
Question
Suppose A, B , and C are events. The probability of A given B , relative to P(|C), is the same as the probability of A given B and C (relative to P ). That is,
Options
- AP(A,B|C) P(B|C) =P(A|B,C)
- BP(A,B|C) P(B|C) =P(B|A,C)
- CP(A,B|C) P(B|C) =P(C|B,C)
- DP(A,B|C) P(B|C) =P(A|C,B)
How the community answered
(18 responses)- A72% (13)
- B17% (3)
- C6% (1)
- D6% (1)
Explanation
From the definition, P(A,B|C) P(B|C) =P(A,B.C)/P(C) P(B.C)/P(C) =P(A,B.C) P(B,C) =P(A|BC) This follows from the definition of conditional probability, applied twice: P(A,B)=(PA|B)P(B)
Topics
#conditional probability#Bayes theorem#probability theory#statistical inference
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