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Joint and conditional probabilities. P(A) = 0.3, P(B) =
Chapter , Problem 2.15(choose chapter or problem)
Joint and conditional probabilities. P(A) = 0.3, P(B) = 0.7
(a) Can you compute P(A and B) if you only know P(A) and P(B)?
(b) Assuming that events A and B arise from independent random processes,
i. What is P(A and B)?
ii. What is P(A or B)?
iii. What is P(A|B)?
(c) If we are given that P(A and B) = 0.1, are the random variables giving rise to events A and B independent?
(d) If we are given that P(A and B) = 0.1, what is P(A|B)?
Questions & Answers
QUESTION:
Joint and conditional probabilities. P(A) = 0.3, P(B) = 0.7
(a) Can you compute P(A and B) if you only know P(A) and P(B)?
(b) Assuming that events A and B arise from independent random processes,
i. What is P(A and B)?
ii. What is P(A or B)?
iii. What is P(A|B)?
(c) If we are given that P(A and B) = 0.1, are the random variables giving rise to events A and B independent?
(d) If we are given that P(A and B) = 0.1, what is P(A|B)?
ANSWER:
Step 1 of 5
(a)
We do not know whether A and B are independent. So we cannot compute P(A and B). If they were Independent then we could.