AMC 8 2020 Problem 13 | Probability Problem

Try this beautiful Problem based on probability from AMC 8 2020.

Probability Problem - AMC 8 2020 Problem 13

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?

6
9
12
18
24

Key Concepts

Percentage

Proportion

Probability

Suggested Book | Source | Answer

Source of the Problem

Answer

AMC 8 2020 Problem 13

9

Try with Hints

Hint 1

Hint 2

Hint 3

At first Let Jamal adds $x$ purple socks,

So, He have $18+x$ purple Socks now, in total He has $36+x$

So probability of drawing a purple sock is $\frac{18+x}{36+x}$

Hence,

$\frac{18+x}{36+x}=\frac{3}{5}$

Probability Problem - AMC 8 2020 Problem 13

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?