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Suppose [tex]\(A\)[/tex] and [tex]\(B\)[/tex] are dependent events. If [tex]\(P(A) = 0.5\)[/tex] and [tex]\(P(B \mid A) = 0.6\)[/tex], what is [tex]\(P(A \cap B)\)[/tex]?

A. 0.6
B. 0.1
C. 0.5
D. 0.3

Sagot :

GinnyAnswer
To solve for [tex]\( P(A \cap B) \)[/tex], we can use the definition of conditional probability and the multiplication rule for dependent events.

We are given:
- [tex]\( P(A) = 0.5 \)[/tex]
- [tex]\( P(B \mid A) = 0.6 \)[/tex]

The formula that relates these probabilities is:
[tex]\[ P(A \cap B) = P(B \mid A) \times P(A) \][/tex]

Plugging in the values provided:
[tex]\[ P(A \cap B) = 0.6 \times 0.5 \][/tex]

Now, multiply the two probabilities:
[tex]\[ P(A \cap B) = 0.3 \][/tex]

Thus, the value of [tex]\( P(A \cap B) \)[/tex] is [tex]\( 0.3 \)[/tex].

So the correct answer is:
[tex]\[ \boxed{0.3} \][/tex]
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