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Question
A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is
Options
\[\frac{3}{16}\]
\[\frac{5}{16}\]
\[\frac{11}{16}\]
\[\frac{14}{16}\]
Solution
\[\text{ Rusted items } =3+5=8\]
\[\text{ Rusted nails } = 3\]
\[\text{ Total nails } = 6\]
\[P\left( \text{ getting a rusted item or a nail } \right) = P\left( \text{ getting a rusted item } \right) + P\left( \text{ getting a nail } \right) - P\left( \text{ getting a rusted item and a nail } \right)\]
\[ = \frac{8}{16} + \frac{6}{16} - \frac{3}{16}\]
\[ = \frac{8 + 6 - 3}{16}\]
\[ = \frac{11}{16}\]
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