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If events A and B are independent, what must be true?
A.) P(AB) = P(B)
B.) P(A/B) = P(A)
C.) P(A) = P(B)
D.) OP(AB) = P(BIA)

Respuesta :

SaniShahbaz

Answer:

Option B s correct. i.e. [tex]P(A|B)=P(A )[/tex]

Step-by-step explanation:

What is the equation of this trend line?

  • When we say that two events let say even A and even B are dependent events, it means one event effects the probability of another event.
  • A dependent event depends on another event. For example, robbing a store and going to prison
  • An independent event does not have any connection to another event’s chances of happening. For example, winning a match, and watching the movie.

Let say A and B are independent events, then we know that

P(A∩B) = P(A) · P(B)

Also we know that the relationship between Probability and Probability B by the following equation [A]

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}.....[A][/tex]

As

P(A∩B) = P(A) · P(B)

Sp,

Putting P(A∩B) = P(A) · P(B) in equation [A]

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

[tex]P(A|B)=\frac{P(A ) . P(B)}{P(B)}[/tex]  

Simplifying,

[tex]P(A|B)=P(A )[/tex]

Therefore, option B s correct.

Keywords: dependent event, independent event, probability

Learn more about dependent event and independent event from brainly.com/question/8246984

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Using conditional probability, it is found that the correct statement is:

B.) P(A/B) = P(A)

Conditional Probability

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

  • P(B|A) is the probability of event B happening, given that A happened.
  • [tex]P(A \cap B)[/tex] is the probability of both A and B happening.
  • P(A) is the probability of A happening.

If two events, A and B, are independent, we have that:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Hence:

[tex]P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{P(A)P(B)}{P(B)} = P(A)[/tex]

Hence, option B is correct.

A similar problem is given at https://brainly.com/question/14398287

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