Question

A drawer contains 50 bolts and 150 nuts. Half of the bolts and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or a bolt?

• A. $\frac{3}{8}$
• B. $\frac{1}{4}$
• C. $\frac{3}{4}$
• D. $\frac{5}{8}$

Answer 1

The correct option is D $\frac{5}{8}$

$P\left(A\right)=$ item chosen is rusted
$=\frac{100}{200}=\frac{1}{2}$
$P\left(B\right)=$ item chosen is bolt $=\frac{50}{200}=\frac{1}{4}$
$P(A\cap B)=$ item is rusted and bolt $=\frac{25}{200}=\frac{1}{8}$
$P(A\cup B)=$ prob. of item is rusted or bolt
$=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$=\frac{1}{2}+\frac{1}{4}-\frac{1}{8}=\frac{5}{8}$