Problem:
Two six-sided dice are fair in the sense that each face is equally likely to turn up. However, one of the dice has the replaced by and the other die has the replaced by . When these dice are rolled, what is the probability that the sum is an odd number?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are equally likely outcomes as shown in the following table.
Exactly of the outcomes have an odd sum. Therefore, the probability is .
The sum is odd if and only if one number is even and the other is odd. The probability that the first number is even and the second is odd is , and the probability that the first is odd and the second is even is . Therefore, the required probability is .