Captain Kirk and Mr. Spock are engaged in a 3-D backgammon playoff, a game employing 6 dice. Kirk asks Spock the probability of rolling the dice and observing 6 sixes. Assume the dice are not biased. Spock's correct a priori reply is _________.
A) "Insufficient data, Captain."
B) "One-sixth to the sixth power, Sir." Translation: (1/6) 6
C) "One-thirtysixth, Sir."
D) "One-thirtysix to the sixth power, Sir." (1/36) 6
E) "The probability is equal to (1/6)X(1/5)X(1/4)X(1/3)X (1/2)X(1/1), Sir." (1/720)

Question

Quizplus · Accepted Answer

The probability of rolling a six on one die is 1/6. Since the rolls are independent, the probability of rolling six sixes in a row is (1/6)^6, which is equivalent to 1/46656. Therefore, Spock's correct reply is "One-sixth to the sixth power, Sir."