At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! 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 help you find accurate solutions to your questions quickly and efficiently.
Sagot :
Certainly! Let's solve this step by step.
Given:
- \( P(A) = 0.4 \)
- \( P(B \mid A) = 0.8 \)
We need to find \( P(A \cap B) \), which is the probability that both events \( A \) and \( B \) occur simultaneously.
From the definition of conditional probability, we know that:
[tex]\[ P(B \mid A) = \frac{P(A \cap B)}{P(A)} \][/tex]
We can rearrange this formula to solve for \( P(A \cap B) \):
[tex]\[ P(A \cap B) = P(B \mid A) \times P(A) \][/tex]
Now, substitute the given values:
[tex]\[ P(A \cap B) = 0.8 \times 0.4 \][/tex]
Multiplying the values, we get:
[tex]\[ P(A \cap B) = 0.32 \][/tex]
Thus, the probability \( P(A \cap B) \) is \( 0.32 \).
The correct answer is:
B. 0.32
Given:
- \( P(A) = 0.4 \)
- \( P(B \mid A) = 0.8 \)
We need to find \( P(A \cap B) \), which is the probability that both events \( A \) and \( B \) occur simultaneously.
From the definition of conditional probability, we know that:
[tex]\[ P(B \mid A) = \frac{P(A \cap B)}{P(A)} \][/tex]
We can rearrange this formula to solve for \( P(A \cap B) \):
[tex]\[ P(A \cap B) = P(B \mid A) \times P(A) \][/tex]
Now, substitute the given values:
[tex]\[ P(A \cap B) = 0.8 \times 0.4 \][/tex]
Multiplying the values, we get:
[tex]\[ P(A \cap B) = 0.32 \][/tex]
Thus, the probability \( P(A \cap B) \) is \( 0.32 \).
The correct answer is:
B. 0.32
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.