A box contains 1000 balls, of which 2 are black and the rest are white. a) Which of the following is most likely to occur in 1000 draws with replacement from the box? fewer than 2 black balls, exactly 2 black balls, more than 2 black balls b) If two series of 1000 draws are made at random from this box, what, approxi- mately, is the chance that they produce the same number of black balls?5. Question 5 Let X be a discrete random variable that takes nonnegative integer values (i.e., 0, 1, 2. ..). Show that E(X) = P(X 2 k). ( Hint: Write P(X > k) as a sum and then (carefully) change the order of summation)