contestada

For events W, X, Y, and Z, the following are true.

P(X|W) = P(Z)
P(YIX) = P(Y)
P(YZ) = P(X)

Given the previous probabilities, what equals to P(X)?
A. P(Z|W)
B. P(Y)
C. P(Z|Y)
D. P(X|Y)
E. P(W|Z)
F. P(Y|X)

Respuesta :

zordanil

Answer:

F. P(Y|X)

Step-by-step explanation:

Let's analyze the given probabilities to determine the value of P(X).

1. P(X|W) = P(Z)

  This tells us that the probability of event X given event W is equal to the probability of event Z.

2. P(Y|X) = P(Y)

  This states that the probability of event Y given event X is equal to the probability of event Y.

3. P(YZ) = P(X)

  This indicates that the joint probability of events Y and Z is equal to the probability of event X.

Based on these probabilities, we can conclude the following:

P(Y|X) = P(Y)

P(YZ) = P(X)

Since P(Y|X) = P(Y), we can deduce that event X has no influence on event Y. Therefore, P(Y) is independent of X.

From P(YZ) = P(X), we can also conclude that the joint probability of events Y and Z is equal to the probability of event X.

Hence, the value of P(X) is equivalent to the joint probability of events Y and Z, which can be expressed as:

P(X) = P(YZ)

Therefore, the answer is F. P(Y|X).

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