List of top Engineering Mathematics Questions asked in GATE XH-C1

Let A and B be two events with probabilities \( P(A) = \frac{3}{4} \) and \( P(B) = \frac{1}{3} \); then which of the following options is true?
Consider that a sample of size 3 is randomly drawn from a population that takes only two values, equally likely: -1 and 1. Let \( z = \max(x_1, x_2, x_3) \) where \( x_1, x_2, x_3 \) are the sample observations. The expected value of \( z \), \( E(z) \) is _________ (round off to two decimal places).