Joint and Conditional Probabilities#
\(P(A) = {{ params.num1 }}\) \(P(B) = {{ params.num2 }}\)
Part 1#
Can you compute \(P(A \cap B)\) if you only know \(P(A)\) and \(P(B)\)?
Answer Section#
Yes
No
Part 2#
Assuming that events \(A\) and \(B\) arise from independent random processes, what is \(P(A \cap B)\)?
Answer Section#
Please enter a numeric value between 0 and 1.
Answer Section#
Please enter a value between 0 and 1.
Part 3#
Assuming that events \(A\) and \(B\) arise from independent random processes, what is \(P(A \cup B)\)?
Answer Section#
Please enter a value between 0 and 1.
Part 4#
Assuming that events \(A\) and \(B\) arise from independent random processes, what is \(P(A|B)\)?
Answer Section#
Please enter a value between 0 and 1.
Part 5#
If we are given that \(P(A \cap B) = {{ params.num3 }}\), are the random variables giving rise to events \(A\) and \(B\) independent?
Answer Section#
Yes
No
Part 6#
If we are given that \(P(A \cap B)\) = \({{ params.num3 }}\), what is \(P(A|B)\)?
Answer Section#
Please enter a value between 0 and 1.
Attribution#
Problem is from the OpenIntro Statistics textbook, licensed under the CC-BY 4.0 license.