QUESTION 1

A student used to buy coffee at Tim Hortons in SITE on a regular basis. Each day he bought two or three cups of coffee, two cups being his choice 50% of the time. Tim Horton's claims that in its "Roll off the rim to win" contest, the winning cups are distributed entirely "at random" with a frequency of one in six. Find (i) the probability that on a given day, the student wins exactly twice, and (ii) that on a given day, the student does not receive a winning cup. Suppose that the choice of buying two or three cups is made independently each day.