Problem: A fair die is rolled six times. The probability of rolling at least a five at least five times is
Answer Choices:
A.
B.
C.
D.
E. none of these
Solution:
Let be the event of rolling at least a five: then the probability of is In six rolls of a die the protability of event happening six times is . The probability of gething exactly five successes and one failure of in a specific order is . Since there are six ways to do this the probability of getting five successes and one failure of A in any order ts . The probability of getting all successes or five successes and one failure in any order is thus .