Probability Help

Question

Of the 24 socks in a drawer, there are three times as many black socks as brown socks. Some of the black socks are plain and some are patterned. There are five times as many plain socks as there are patterned socks. What is the probability that, without looking, you select a plain sock from the drawer ?

 

A. 1/4

B. 5/8

C. 5/6

D. 3/4

Answer 1

Let x be the number of brown socks

 

3x + x = 24; hence x = 6; therefore there 6 brown socks and 18 black socks

 

Let y be number of patterned socks; of the 18 black socks; 5y + y = 18; hence y = 3, there are therefore 3 patterned socks and 15 plain socks

 

Hence there are in totality: Brown socks = 6; Patterned socks = 3; and plain socks = 15

 

probability of randomly selecting a plain black socks = 15/24 = 5/8 (B)