youre at a clothing store that dyes your clothes while you wait. you get to pick from 4 pieces of clothing…

youre at a clothing store that dyes your clothes while you wait. you get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange). if you randomly pick the piece of clothing and the color, what is the probability that youll end up with socks that arent blue?

youre at a clothing store that dyes your clothes while you wait. you get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange). if you randomly pick the piece of clothing and the color, what is the probability that youll end up with socks that arent blue?

Answer

Explanation:

Step1: Calculate total combinations

The total number of combinations of clothing - piece and color is the product of the number of clothing - pieces and the number of colors. There are 4 pieces of clothing and 3 colors, so the total number of combinations is $4\times3 = 12$.

Step2: Determine favorable combinations

We want socks that aren't blue. There is 1 pair of socks, and there are 2 non - blue colors (purple and orange). So the number of favorable combinations is $1\times2=2$.

Step3: Calculate probability

The probability $P$ is the number of favorable combinations divided by the total number of combinations. So $P=\frac{2}{12}=\frac{1}{6}$.

Answer:

$\frac{1}{6}$