A fair die is rolled six times. The probability of rolling more than 4 at least five times is
(a) 2/729 b) 3/729 c) 12/729 d) 13/729 (e) none of the above
We want the probability that when the die is rolled six times we get 5 sucesses, , or 6 successes, .
For we want 5 successes and 1 failure. The failure can occur on any one of the 6 rolls. So .
For we must have all 6 successes. So .
Therefore the probability that one or other of these events occurs is