BTGmoderatorDC wrote:If a light bulb is selected at random from a shipment, what is the probability that the light bulb is defective?
(1) The ratio of the number of defective light bulb_s to the number of nondefective light bulb_s is 1 to 60.
(2) The shipment contains 720 light bulb_s.
Source: Magoosh
$$? = {{\# \,\,{\rm{defective}}\,\,{\rm{bulb_s}}} \over {\# \,\,{\rm{total}}\,\,{\rm{bulb_s}}}}$$
$$\left( 1 \right)\,\,\left\{ \matrix{
\,\# \,\,{\rm{defective}}\,\,{\rm{bulb_s}} = k \hfill \cr
\,\# \,\,{\rm{non}} - {\rm{defective}}\,\,{\rm{bulb_s}} = 60k \hfill \cr} \right.\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = {k \over {61k}} = {1 \over {61}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}.$$
$$\left( 2 \right)\,\,\# \,\,{\rm{total}}\,\,{\rm{bulb_s}} = 720\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\# \,\,{\rm{defective}}\,\,{\rm{bulb_s}} = 1\,\,\,\, \Rightarrow \,\,\,? = {1 \over {720}} \hfill \cr
\,{\rm{Take}}\,\,\# \,\,{\rm{defective}}\,\,{\rm{bulb_s}} = 2\,\,\,\, \Rightarrow \,\,\,? = {2 \over {720}} \hfill \cr} \right.$$
The correct answer is therefore (A).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
