Which expression correctly defines P(B|A)?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $24.99Unlock all

Enhance your understanding of Descriptive Statistics and Probability. Study with interactive questions and detailed explanations. Prepare effectively for your test!

Multiple Choice

Which expression correctly defines P(B|A)?

Explanation:
Conditional probability asks what the chance of B is when we already know A has occurred. It is defined as P(B|A) = P(A ∩ B) / P(A), provided P(A) > 0. Intuitively, you’re focusing only on the outcomes where A happened and asking what fraction of those also include B. The numerator counts the outcomes where both A and B occur, while the denominator counts all outcomes where A occurs. This is different from the probability of A given B, which uses P(B) in the denominator, and from the idea of independence, which states P(A ∩ B) = P(A)P(B). It also differs from the union rule, P(A ∪ B) = P(A) + P(B) − P(A ∩ B). The given expression is precisely the definition of P(B|A).

Conditional probability asks what the chance of B is when we already know A has occurred. It is defined as P(B|A) = P(A ∩ B) / P(A), provided P(A) > 0. Intuitively, you’re focusing only on the outcomes where A happened and asking what fraction of those also include B. The numerator counts the outcomes where both A and B occur, while the denominator counts all outcomes where A occurs. This is different from the probability of A given B, which uses P(B) in the denominator, and from the idea of independence, which states P(A ∩ B) = P(A)P(B). It also differs from the union rule, P(A ∪ B) = P(A) + P(B) − P(A ∩ B). The given expression is precisely the definition of P(B|A).

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy