Suppose there are three events then which formula must always be equal to P(E1|E2,E3)?

The correct answer is B. P(E1,E2;E3)/P(E2,E3). This is an application of conditional probability: P(E1,E2)=P(E1|E2)P(E2). so P(E1|E2) = P(E1,E2,E3)/P(E2,E3) If the events are A and B respectively, this is said to be "the probability of A given B" It is commonly denoted by P(A|B): or sometimes PB(A). In case that both "A"…

Statistics and Probability

Question

Options

AP(E1,E2,E3)P(E1)/P(E2:E3)
BP(E1,E2;E3)/P(E2,E3)
CP(E1,E2|E3)P(E2|E3)P(E3)
DP(E1,E2|E3)P(E3)
EP(E1,E2,E3)P(E2)P(E3)

How the community answered

(36 responses)

A
17% (6)
B
72% (26)
C
3% (1)
D
6% (2)
E
3% (1)

Explanation

This is an application of conditional probability: P(E1,E2)=P(E1|E2)P(E2). so P(E1|E2) = P(E1,E2,E3)/P(E2,E3) If the events are A and B respectively, this is said to be "the probability of A given B" It is commonly denoted by P(A|B): or sometimes PB(A). In case that both "A" and "B" are categorical variables, conditional probability table is typically used to represent the conditional probability.

Topics

#conditional probability#joint probability#probability axioms#probability decomposition

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