If we roll a pair of fair dice and count the number of aces (one dot) showing, the probability model is as follows:

Back in the 17th century, some gamblers thought that the probability of at least one ace (i.e., one or more aces) when rolling two dice was 1/6 + 1/6. Is that true?
A) Yes.
B) No, it's larger than 1/6 + 1/6.
C) No, it's smaller than 1/6 + 1/6.
D) Sometimes it's larger and sometimes it's smaller.
E) Impossible to say.

Question

If we roll a pair of fair dice and count the number of aces (one dot) showing, the probability model is as follows:

Back in the 17th century, some gamblers thought that the probability of at least one ace (i.e., one or more aces) when rolling two dice was 1/6 + 1/6. Is that true?
A) Yes. 
B) No, it's larger than 1/6 + 1/6. 
C) No, it's smaller than 1/6 + 1/6. 
D) Sometimes it's larger and sometimes it's smaller. 
E) Impossible to say.

Quizplus · Accepted Answer

The probability of getting at least one ace is equal to 1- probability of getting no aces. The probability of getting no aces is (5/6)*(5/6) = 25/36. Therefore, the probability of getting at least one ace is 1-25/36 = 11/36, which is smaller than 1/6 + 1/6 = 1/3.

If We Roll a Pair of Fair Dice and Count