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, then find the probability that it is rusted or is a nail

• A. $\frac{13}{16}$
• B. $\frac{7}{8}$
• C. $\frac{9}{16}$
• D. $\frac{11}{16}$

Answer 1

The correct option is D $\frac{11}{16}$

The total number of nails and nuts is $16.$
Let $R$ be the event for rusted
$P\left(R\right)=\frac{8}{16}=\frac{1}{2}$
Let $N$ be the event for nails.
$P\left(N\right)=\frac{6}{16}=\frac{3}{8}$
$P(R\cap N)=\frac{3}{16}$
$(\because 3\text{nails are rusted})$
$\therefore P(R\cup N)=P\left(R\right)+P\left(N\right)-P(R\cap N)$
$\Rightarrow P(R\cup N)=\frac{1}{2}+\frac{3}{8}-\frac{3}{16}=\frac{11}{16}$