Bob is asked to construct a probability model for rolling a pair of fair dice. He lists the outcomes as \( 2,3,4,5,6,7,8,9,10,11,12 \). Because there are 11 outcomes, he reasoned, the probability of rolling two must be \( \frac{1}{11} \). What is wrong with Bob's reasoning? Choose the correct answer below. A. The sum of the probabilities of all outcomes does not equal 1 . B. The experiment does not have equally likely outcomes. C. The probability of an event is less than 0 . D. The probability of an event is greater than 1 . E. There is nothing wrong with Bob's reasoning.

Bob's reasoning falls short because there are actually not 11 outcomes when rolling a pair of dice! Each die has 6 faces, so when you roll two dice, there are a total of \(6 \times 6 = 36\) possible outcomes. This means that the probabilities he assigned to each possible sum are based on incorrect calculations. To find the correct probability of rolling a sum of 2, for instance, you note that there's only 1 way this can happen (1+1). Thus, the correct probability should be calculated as the number of favorable outcomes divided by 36. Bob should have listed all possible outcomes and considered their frequencies to build an accurate probability model!