Discussion

If you roll a pair of dice, what is the probability that (at least) one of the dice is a 4 or the sum of the dice is 7?

Answer: D

Let \( A \) be "at least one die shows 4" and \( B \) be "the sum is 7", over the 36 outcomes.

\[ |A| = 11 \quad (\text{six with the first a 4, six with the second, less the double-counted } (4,4)) \]

\[ |B| = 6: \ (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) \]

\[ |A \cap B| = 2: \ (3,4),(4,3) \]

\[ |A \cup B| = 11 + 6 - 2 = 15 \quad\Longrightarrow\quad P = \frac{15}{36} \]

Both corrections matter: \( (4,4) \) within \( A \), and the two outcomes shared by \( A \) and \( B \).

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