Discussion
If two dice are thrown, what is the probability that the sum is neither 7 nor 11 ?
Answer: C
The probability is \(\frac{7}{9}\).
With two dice there are 36 equally likely outcomes. A sum of 7 occurs in 6 ways and a sum of 11 in 2 ways (5-6 and 6-5), so 8 outcomes are excluded:
\[ \begin{aligned} P &= 1 - \frac{6 + 2}{36} \\ &= \frac{28}{36} = \frac{7}{9} \end{aligned} \]
The chance that the sum is 7 or 11 is \(\frac{8}{36} = \frac{2}{9}\); the question asks for the complement. \(\frac{1}{9}\), \(\frac{3}{9}\) and \(\frac{5}{9}\) do not match either count, so only \(\frac{7}{9}\) fits.
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