25. Probability question bank (Maths)

A fair die is rolled. Consider the events \( A = \{1, 3, 5\} \), \( B = \{2, 3\} \) and \( C = \{2, 3, 4, 5\} \). Then the conditional probability \( P((A \cup B)\,|\,C) \) is

Let \( n_1 \) and \( n_2 \) be the number of red and black balls, respectively, in box I. Let \( n_3 \) and \( n_4 \) be the number of red and black balls, respectively, in box II.

One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box II is \( 1/3 \), then the correct option(s) with the possible values of \( n_1, n_2, n_3, n_4 \) is(are):