A Box Contains Blue Chips and Red Chips $\frac { 1 } { 4 }$

Multiple Choice

A box contains blue chips and red chips. A person selects two chips without replacement. If the probability of selecting a blue chip and a red chip is $\frac { 1 } { 4 }$ , and the probability of selecting a blue chip on the first draw is $\frac { 5 } { 16 }$ , find the probability of selecting the red chip on the second draw, given that the first chip selected was a blue chip.

A) $\frac { 2 } { 5 }$
B) $\frac { 3 } { 5 }$
C) $\frac { 4 } { 5 }$
D) $\frac { 1 } { 5 }$