Question

Jamal has a drawer containing 6 green socks, 18 purple socks, and 12 orange socks. After

adding more purple socks, Jamal noticed that there is now a 60% chance that a sock randomly
selected from the drawer is purple. How many purple socks did Jamal add?
(A) 6
(B) 9
(C) 12
(D) 18
(E) 24

Answer 1

Jamal added 9 purple sox

Explanation:

Here, we want to increase the probability

Initially the probability is;

18/(6 + 18 + 12) = 18/36 = 1/2 or 0.5 or 50%

So now, the probability is 60% which is 60/100 or 0.6

If we added x socks, then we number of purple socks become (18 + x)

The total number of x will be (36 + x)

so the probability now will be;

18+x/36 + x = 0.6

18 + x = 0.6(x + 36)

18 + x = 0.6x + 21.6

x-0.6x = 21.6-18

0.4x = 3.6

x = 3.6/0.4

x = 9