List of top Statistics Questions on Conditional probability asked in IIT JAM MS

A retail shop sells three brands of tea, namely Brand A, Brand B, and Brand C, and each in two varieties, namely regular and premium. The proportion of customers buying the Brands A, B, and C are \(40\%\), \(35\%\), and \(25\%\), respectively. Out of those customers who buy Brand A, \(30\%\) buy the premium variety, out of those who buy Brand B, \(40\%\) buy the premium variety, while out of those who buy Brand C, \(60\%\) buy the premium variety. Given that a randomly selected customer has bought the premium variety of tea, the probability that he/she has bought Brand B equals

Let \( X \) and \( Y \) be continuous random variables with the joint probability density function 

Then \( E(X | Y = -1) \) equals} 
 

Let \( E \) and \( F \) be two events with \( 0<P(E)<1 \), \( 0<P(F)<1 \) and \( P(E) + P(F) \geq 1 \). Which of the following statements is (are) TRUE?