Answered

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[tex]$A$[/tex] and [tex]$B$[/tex] are independent events.

[tex]\[
\begin{array}{l}
P(A) = 0.30 \\
P(B) = 0.40
\end{array}
\][/tex]

What is [tex]\(P(A \mid B)\)[/tex]?

A. 0.40

B. 0.30

C. 0.12

D. Not enough information

Sagot :

GinnyAnswer
In probability theory, when two events [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are independent, the occurrence of one event does not affect the probability of the occurrence of the other event. This independence can be expressed mathematically:

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

This formula states that the probability of [tex]\(A\)[/tex] given that [tex]\(B\)[/tex] has occurred, denoted [tex]\(P(A \mid B)\)[/tex], is equal to the probability of [tex]\(A\)[/tex] because the occurrence of [tex]\(B\)[/tex] does not impact [tex]\(A\)[/tex].

Given:
[tex]\[ P(A) = 0.30 \][/tex]
[tex]\[ P(B) = 0.40 \][/tex]

Since [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are independent:

[tex]\[ P(A \mid B) = P(A) = 0.30 \][/tex]

Hence, the correct answer is:
[tex]\[ \boxed{0.30} \][/tex]
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