For any two events A and B, if P(A|B) = 0.6 and P(B|A) = 0.4, then what is the value of P(A)/P(B)?
1.5
We are given \(P(A\mid B) = 0.6\) and \(P(B\mid A) = 0.4\), and we need to find \(\dfrac{P(A)}{P(B)}\).
By the definition of conditional probability:
\(P(A\mid B) = \dfrac{P(A\cap B)}{P(B)}\) and \(P(B\mid A) = \dfrac{P(A\cap B)}{P(A)}\).
Dividing the first by the second, the common factor \(P(A\cap B)\) cancels:
\(\dfrac{P(A\mid B)}{P(B\mid A)} = \dfrac{P(A\cap B)/P(B)}{P(A\cap B)/P(A)} = \dfrac{P(A)}{P(B)}\).
Therefore \(\dfrac{P(A)}{P(B)} = \dfrac{0.6}{0.4} = 1.5\).
Hence, the correct answer is 1.5.
Important Questions from Conditional Probability
Let A and B be two events such that \(P(\overline{A \cup B}) = \dfrac{1}{6}\) , P(A ∩ B) = \(\dfrac{1}{4}\) and P(A̅) = \(\dfrac{1}{4}\) , where A̅ stands for complement of event A. Then, events A and B are:
A bike manufacturing factory has two plants P and Q. Plant P manufactures 60 percent of bikes and plant Q manufacture 40 percent. 80 percent of the bikes at plant P and 90 percent of the bikes at plant Q are rated of standard quality. A bike is chosen at random and is found to be of standard quality. What is the probability that it has come from plant P?
A and B are two events such that A̅ and B̅ are mutually exclusive. If P(A) = 0.5 and P(B) = 0.6, then what is the value of P(A|B)?
For two dependent events A and B, it is given that P(A) = 0.2 and P(B) = 0.5. If A ⊆ B, then the values of conditional probabilities P(A|B) and P(B|A) are respectively
In a bulb factory, machines P, Q and R manufacture respectively 25%, 35% and 40% of the total. Of their output 5, 4 and 2 percent respectively are defective bulbs. A bulb is drawn at random and it is found to be defective. What is the probability that it was manufactured by machine Q?
