Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Suppose [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are dependent events. If [tex]\( P(A) = 0.3 \)[/tex] and [tex]\( P(B \mid A) = 0.9 \)[/tex], what is [tex]\( P(A \cap B) \)[/tex]?

A. 0.6
B. 0.9
C. 0.3
D. 0.27

Sagot :

GinnyAnswer
To find [tex]\( P(A \cap B) \)[/tex], which is the probability that both events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] occur simultaneously, we use the conditional probability formula. This is given by:

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

Here, we are given:
- [tex]\( P(A) = 0.3 \)[/tex]
- [tex]\( P(B \mid A) = 0.9 \)[/tex]

Substituting these values into the formula:

[tex]\[ P(A \cap B) = 0.3 \cdot 0.9 \][/tex]

[tex]\[ P(A \cap B) = 0.27 \][/tex]

So, the probability that both events [tex]\( A \)[/tex] and [tex]\( B \)[/tex] occur is [tex]\( 0.27 \)[/tex].

Therefore, the correct answer is:
[tex]\[ \boxed{0.27} \][/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.